1. Which Is The Smallest No Divides 2880 And Gives A Perfect Square?
A.1 B.2 C.5 D.6
Ans: C
2. Two Bowls Are Taken, One Contains Water And Another Contains Tea Equal Amount . One Spoon Of Water From 1st Is Added To Second Bowl And Mixed Well, And A Spoon Of Mixture Is Taken From Second Bowl And Added To The 1st Bowl. Which Statement Will Hold Good For The Above?
{
Thought Process :
Water Bowl Tea Bowl
100 100
90w (+10w= Spoon Volume) 100tea+10water
90w+ (10*10/11)Tea+ 10/11 W 100t- (10*10/11) T
+ 10w- 10/11w
(1st Bowl’s Water Volume Is Equal To 2nd Bowls Tea Volume)
3. Form 8 Digit Numbers From By Using 1, 2,3,4,5 With Repetition Is Allowed And Must Be Divisible By 4?
A.31250 B.97656 C.78125 D.97657
Ans: C
4. Rearrange And Categorize The Word ‘Rapeteka’?
Ans: Bird
5. One Problem On (785^3-235^3)/(785^2+785*235+235^2)
Ans: You Are Free To Carry A Calculator With You But You Should Not Use It To Solve This Kind Of Problem. Because It Is Simple:
A3-b3 / A2+ab+b2
Ans Is : A-b Here 785-235= 550 That's It.
6. In School There Are Some Bicycles And 4 Wheeler Wagons. One Tuesday There Are 190 Wheels In The Campus. How Many Bicycles Are There?
Ans: 15
Thought Process : B*2+w*4=190 I.E. , B+2w=95 Now See U Can Not Solve 2 Unknowns From 1 Equation, So Just Plot Options Here To Get The Right Answer And Verify If You Are Getting Integers As Values Of B And W.
7. There Are Two Persons Paul And Jay .Paul Lies On Monday, Tuesday, Wednesday And The Remaining Days He Speaks Truth. Jay Lies On Thursday, Friday, Saturday And The Remaining Days He Speaks Truth. Once They Meet Each Other, In Their Conversation Paul Says That Yesterday Is The Day One Among Those I Lie. Jay Also Says That Yesterday I Also Lie. What Is That Day?
A) Sunday. B) Tuesday. C) Thursday. D) Wednesday
[Thought Process: Now This Day Cannot Be Sunday Because In Monday Paul Speaks Truth And Sunday Everyone Tells Truth. So It Must Be Weekdays. Again, Tuesday Can Not Possible Because Monday And Tuesday Paul Speaks Truth. In Case Of Thrust Day, Paul Speaks Lie And Wednesday He Speaks True. And Joy Speaks Truth In Thursday And He Speak Lies In Wednesday. So, Thursday Is The Answer.
8. A Father Has 7 Penny’s With Him And 1 Water Melon Is For 1p, 2chickoos For 1p, 3 Grapes Foe 1p. He Has Three Sons. How Can He Share The Fruits Equally?
Ans: 1 Watermelon, 2chickoos, 1grape
9. (1/2) Of A Number Is 3 Times More Than The (1/6) Of The Same Number?
Ans: 9
10. There Are Two Pipes A And B. If A Filled 10 Liters In Hour B Can Fills 20 Liters In Same Time. Likewise B Can Fill 10, 20, 40, 80,160…. If B Filled In (1/16) Th Of A Tank In 3 Hours, How Much Time Will It Take To Fill Completely?
Ans: 7 Hours
11.A certain pump can drain a full 375-gallon tank in 15 minutes. At this rate, how many more minutes would it take to drain a full 600-gallon tank?
(A) 9 (B) 15 (C) 18 (D) 24 (E) 25
12. If n is an even integer, which of the following must be an odd integer?
(A) 3n-2 (B) 3(n+1) (C)n-2 (D)n/3 (E)n^2
13. Cindy has a collection of 80 records. If 40 percent of her records are jazz records, and the rest are blues records, how many blues records does she have?
(A) 32
(B) 40
(C) 42
(D) 48
(E) 50
14. Express 2,750,389 in scientific notation.
(A) 27.50389 x 105
(B) 275.0389 x 103
(C) 27.50389 x 106
(D) 0.2750389 x 107
(E) 2.750389 x 106
15. A rectangle and a triangle have equal areas. The length of the rectangle is 12 inches, and its width is 8 inches. If the base of the triangle is 32 inches, what is the length, in inches, of the altitude drawn to the base?
(A) 6
(B) 8
(C) 9
(D) 12
(E) 16
16. If the area of a triangle is 24 and its base is 6, what is the length of the altitude to that base?
(A)3 (B)6 (C)8 (D)10 (E)unknown
17.Lenny's average score after 3 tests is 88. What score on the 4th test would bring Lenny's average up to exactly 90?
(A)92 (B)93 (C)94 (D)95 (E)96
18. If an integer is divisible by 6 and by 9, then the integer must be divisible by which of the following?
A. 12
B. 18
C. 24
D. 36
E. 54
19.If Jeff and Jimmy have less than 22 dollars between them, and Jeff has 8 dollars, which of the following could be the number of dollars that Jimmy has?
I.12 II. 14 III. 16
A. I only
B. III only
C. I & III.
D. I & II
E. Neither I, II, nor III are correct
20.Stephanie drove at an average rate of 50 miles per hour for two hours and then increased her average rate by 50% for the next 3 hours. Her average rate of speed for the 5 hours was t miles per hour. What is the value of t?
A. 55 mph
B. 60 mph
C. 65 mph
D. 70 mph
E. 75 mph
21. How many complete tanks of water, each with a capacity of 3 cubic meters, are needed to fill an empty cylindrical tank whose height is 3 meters and whose base has a radius of 2 meters?
A) 12 B) 13 C) 14 D) 15 E) 16
22. Any serious policy discussion about acceptable levels of risk in connection with explosions is not well served if the participants fail to use the word “explosion” and use the phrase “energetic disassembly” instead. In fact, the word “explosion” elicits desirable reactions, such as a heightened level of attention, whereas the substitute phrase does not. Therefore, of the two terms, “explosion” is the one that should be used throughout discussions of this sort.
Which of the following is an assumption on which the argument above depends?
(A) In the kind of discussion at issue, the advantages of desirable reactions to the term “explosion” outweigh the drawbacks, if any, arising from undesirable reactions to that term.
(B) The phrase “energetic disassembly” has not so far been used as a substitute for the word “explosion” in the kind of discussion at issue.
(C) In any serious policy discussion, what is said by the participants is more important than how it is put into words.
(D) The only reason that people would have for using “energetic disassembly” in place of “explosion” is to render impossible any serious policy discussion concerning explosions.
(E) The phrase “energetic disassembly” is not necessarily out of place in describing a controlled rather than an accidental explosion
23. A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one-gallon or half- gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
(A) 2 (B) 2 ½ (C) 3 (D) 3 ½ (E) 4
24. To buy a computer system, a customer can choose one of 4 monitors, one of 2 keyboards, one of 4 computers and one of 3 printers. Determine the number of possible systems that a customer can choose from.
(A) 96 (B)98 (C)98.5 (D) 94 (E)100
25. A student can select one of 6 different mathematics books, one of 3 different chemistry books and one of 4 different science books. In how many different ways can a student select a book of mathematics, a book of chemistry and a book of science?
A) 14 (B)12 (C)72 (D) 74 (E)76
Showing posts with label General Aptitude. Show all posts
Showing posts with label General Aptitude. Show all posts
Tuesday, October 25, 2011
Monday, October 24, 2011
TCS Recruitment Questions
QUESTION NO 1::
Rearrange the following letters to make a word and choose the category in which it fits.
RAPETEKA
a. city
b. fruit
c. bird
d. vegetable
Correct answer: bird (parakeet)
QUESTION NO 2::
A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the hare in the other. The hare starts after the tortoise has covered 1/5 of its distance and that too leisurely. The hare and tortoise meet when the hare has covered only 1/8 of the distance. By what factor should the hare increase its speed so as to tie the race?
a. 8
b. 37.80
c. 5
d. 40
ANS :37.80
QUESTION NO 3::
There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one litre every hour in A, it gets filled up like 10, 20, 40, 80, 160... in tank B. (At the end of first hour, B has 10 litres , second hour it has 20, and so on). If tank B is 1/32 filled after 21 hours, what is the total duration required to fill it completely?
a. 26 hrs
b. 25 hrs
c. 5 hrs
d. 27 hrs
ANS:26 hrs
A similar question with numbers changed --
QUESTION NO 4::
Anoop managed to draw 7 circles of equal radii with their centres on the diagonal of a square such that the two extreme circles touch two sides of the square and each middle circle touches two circles on either side. Find the ratio of the radius of the circles to the side of the square.
a. (2+ 7√2):1
b. 1:(2+ 6√2)
c. 1:(4+ 7√3)
d. 1:(2+ 7√2)
ANS: b
QUESTION NO 5:
A sheet of paper has statements numbered from 1 to 30. For all values of n from 1 to 30, statement n says "At most n of the statements on this sheet are false". Which statements are true and which are false?
a. The even numbered statements are true and the odd numbered are false.
b. All statements are false.
c. All statements are true.
d. The odd numbered statements are true and the even numbered are false.
ANS: b
QUESTION NO 6::
Ferrari S.p.A. is an Italian sports car manufacturer based in Maranello, Italy. Founded by Enzo Ferrari in 1928 as Scuderia Ferrari, the company sponsored drivers and manufactured race cars before moving into production of street-legal vehicles in 1947 as Ferrari S.p.A.. Throughout its history, the company has been noted for its continued participation in racing, especially in Formula One, where it has enjoyed great success. Rohit once bought a Ferrari. It could go 2 times as fast as Mohit's old Mercedes. If the speed of Mohit's Mercedes is 32 km/hr and the distance travelled by the Ferrari is 952 km, find the total time taken in hours for Rohit to drive that distance.
a. 29.75
b. 14.88
c. 15.88
d. 476
ANS: b
QUESTION NO 7::
On the planet Oz, there are 8 days in a week- Sunday to Saturday and another day called Oz day. There are 36 hours in a day and each hour has 90 min while each minute has 60 sec. As on earth, the hour hand covers the dial twice every day.
Find the approximate angle between the hands of a clock on Oz when the time is 12:40 am.
a. 251
b.111
c.71
d.89
ANS: d
QUESTION NO :: 8
For the FIFA world cup. Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B,Paul picks A with the same probability as A’s chance of winning. Let’s assume such rumors to be true and than in match between Ghana and Bolivia, Ghana the stronger team has a probability of 2/3 of winning the game.
What is the probability that paul will correctly pick the winner of the Ghana-Bollivia game ?
a.5/9
b.4/9
c.1/9
d.2/3
ANS : a
QUESTION NO::9
Alok and Bhanu play the following min-max game. Given the expression N = 9 +X + Y– Z where X, Y and Z are variables representing single digits (0 to 9), Alok would like to maximize N while Bhanu
would like to minimize it. Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X, Y or Z). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the value for the remaining variable. Assuming both play to their optimal
strategies, the value of N at the end of the game would be
a. 27
b. 18
c. 20
d. 0.0
ANS: b
QUESTION NO::10
Alok and Bhanu play the following min-max game. Given the expression N = X– Y – Z where X, Y and Z are variables representing single digits (0 to 9), Alok would like to maximize N while Bhanu would like to minimize it. Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X, Y or Z). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the value for the remaining variable. Assuming both play to their optimal strategies, the value of N at the end of the game would be
a. 2
b. 4
c. 9
d. -18
QUESTION NO::11
Alok and Bhanu play the following min-max game. Given the expression N = 38 + X*(Y – Z) where X, Y and Z are variables representing single digits (0 to 9), Alok would like to maximize N while Bhanu would like to minimize it. Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X, Y or Z). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the value for the remaining variable. Assuming both play to their optimal strategies, the value of N at the end of the game would be
a.38
b.119
Similar question with numbers changed --
d.30
QUESTION NO::12
A person drives with constant speed and after some time he sees a milestone with 2 digits. Then travels for 1 hours and sees the same 2 digits in reverse order. 1 hours later he sees that the milestone has the same 2 digits with a 0 between them. What is the speed of the car?
a.54.00 mph
b.45.00 mph
c.27.00 mph
d.36.00 mph
ANS: b
s=speed
"Then travels for 1 hour and sees the same 2 digits in reverse order."
10x + y + 1s = 10y + x
10x - x + s = 10y - y
9x + s = 9y
1 hours later he sees that the milestone has the same 2 digits with a 0 between them."
10y + x + s = 100x + y
10y - y + s = 100x - x
9y + s = 99x
Rearrange the above two equations for elimination
9x - 9y + s = 0
-99x+9y + s = 0
----------------adding eliminates y
-90x + 2s = 0
2s = 90x
s = 45x
x has to equal 1, then s = 45 mph (If x=2 and s=90 mph, when added to
a two digit milestone, could not be at another two digit milestone.)
QUESTION NO::13
Fermat’s Last Theorem is a statement in number theory which states that it is impossible to separate any power higher than the second into two like powers, or, more precisely- If an integer n is greater than 2, then the equation a^n b^n = c^n has no solutions in non-zero integers a, b, and c. Now, if the difference of any two numbers is 9 and their product is 17, what is the sum of their squares?
a.43
b.45
c.98
d.115
ANS: d
QUESTION NO::14
India with a burgeoning population and a plethora of vehicles (at last count there were more than 20 million of them) has witnessed big traffic jams at all major cities. Children often hone their counting skills by adding the wheels of vehicles in schoolyards or bus depots and guessing the number of vehicles.
Alok, one such child, finds only bicycles and 4 wheeled wagons in his schoolyard. He counts the totalnumber of wheels to be 46. What could be the possible number of bicycles?
a.25
b.5
c.4
ANS: b
QUESTION NO::15
Alchemy is an occult tradition that arose in the ancient Persian empire. Zosimos of Panopolis was an early alchemist. Zara, reads about Zosimos and decides to try some experiments. One day, she collects two buckets, the first containing one litre of ink and the second containing one litre of cola. Suppose she takes one cup of ink out of the first bucket and pours it into the second bucket. After mixing she takes one cup of the mixture from the second bucket and pours it back into the first bucket. Which one of the following statements holds now?
a.There is more cola in the first bucket than ink in the second bucket.
b.There is as much cola in the first bucket as there is ink in the second bucket.
c.There is less cola in the first bucket than ink in the second bucket.
ANS:c
QUESTION NO:: 16
Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line; i.e. the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The maximum value of n1(P) over all configurations P of 19 points in the plane is
a.10
b.9
c.3
d.5
ANS : The options given are wrong, the answer would be 19. Or it can be taken as the maximum value, making a. here.
QUESTION NO :: 17
15 suspects are rounded by the police and questioned about a bank robbery. Only one of them is guilty. The suspects are made to stand in a line and each person declares that the person next to him on his right is guilty. The rightmost person is not questioned. Which of the following possibilities are true?
A. All the suspects are lying or leftmost is innocent
B. All the suspects are lying and leftmost is innocent
a.A only
b.B only
c.A and B
d.Neither A and B
ANS : a
Considering that all are lying that "The one to my right is guilty" literally means than 2-15 are innocent. If they are all lying, leftmost should be guilty.
QUESTION NO::18
Alchemy is an occult tradition that arose in the ancient Persian empire. Zosimos of Panopolis was an early alchemist. Zara, reads about Zosimos and decides to try some experiments. One day, she collects two buckets, the first containing one litre of ink and the second containing one litre of cola. Suppose she takes one cup of ink out of the first bucket and pours it into the second bucket. After mixing she takes one cup of the mixture from the second bucket and pours it back into the first bucket. Which one of the following statements holds now?
a.There is more cola in the first bucket than ink in the second bucket.
b.There is as much cola in the first bucket as there is ink in the second bucket.
c.There is less cola in the first bucket than ink in the second bucket.
ANS: c
QUESTION NO ::19
Both A and B Alice and Bob play the following chip-off-the-table game. Given a pile of 58 chips, Alice first picks at least one chip but not all the chips. In subsequent turns, a player picks at least one chip but no more than the number picked on the previous turn by the opponent. The player to pick the last chip wins. Which of the following is true?
a.In order to win, Alice should pick 14 chips on her first turn.
b.In order to win, Alice should pick two chips on her first turn.
c.In order to win, Alice should pick one chip on her first turn.
QUESTION NO ::20
30 teams enter a hockey tournament. A team is out of the tournament if it loses 2 games. What is the maximum number of games to be played to decide one winner?
a.60
b.59
c.61
d.30
e.34
ANS: b
29 teams have to fail two games, so 29*2=58, the winner loses one game. Therefore 58+1=59.
QUESTION NO::21
Suppose 12 monkeys take 12 minutes to eat 12 bananas. How many monkeys would it take to eat 72 bananas in 72 minutes?
a.6
b.72
c.12
ANS: c
QUESTION NO::22
Alok is attending a workshop “How to do more with less” and today’s theme is Working with fewer digits . The speakers discuss how a lot of miraculous mathematics can be achieved if mankind (as well as
womankind) had only worked with fewer digits. The problem posed at the end of the workshop is How many 5 digit numbers can be formed using the digits 1, 2, 3, 4, 5 (but with repetition) that are divisible by 4? Can you help Alok find the answer?
a.625
b.375
c.230
d.500
ANS: a
QUESTION NO::23
A and B play a game of dice between them. The dice consist of colors on their faces (instead of numbers). When the dice are thrown, A wins if both show the same color; otherwise B wins. One die has 4 red face and 2 blue faces. How many red and blue faces should the other die have if the both players have the same chances of winning?
a.3 red and 3 blue faces
b.2 red and remaining blue
c.6 red and 0 blue
d.4 red and remaining blue
ANS: a
QUESTION NO::24
A sheet of paper has statements numbered from 1 to 45. For all values of n from 1 to 45, statement n says “At most n of the statements on this sheet are false”. Which statements are true and which are false?
a.The odd numbered statements are true and the even numbered are false.
b.The even numbered statements are true and the odd numbered are false.
c.All statements are false.
QUESTION NO:: 25
All statemeThere are two containers A and B. A is half filled with wine whereas B which is 3 times the size of A contains one quarter portion wine. If both containers are filled with water and the contents are poured into container C, what portion of container C is wine?
a. .30
b. .31
c. .42
d. .25
QUESTION NO:: 25
A and B play a game of dice between them. The dice consist of colors on their faces (instead of numbers). When the dice are thrown, A wins if both show the same color; otherwise B wins. One die has 3 red faces and 3 blue faces. How many red and blue faces should the other die have if the both players have the same chances of winning?
a.5 red and 1 blue faces
b.1 red and 5 blue faces
c.3 red and 3 blue faces
QUESTION NO:: 27
A circular dartboard of radius 1 foot is at a distance of 20 feet from you. You throw a dart at it and it hits the dartboard at some point Q in the circle. What is the probability that Q is closer to the center of the circle than the periphery?
a.0.75
b.1
c.0.5
d.0.25
Ans:.25
Here the data about the distance is of no use.
For radius of 1 m if dart is inside the circle of 1/2 m radius the dart is closer to center than periphery
so area of 1/2 m circle is pie/4
area of board is pie
So probability = 0.25
QUESTION NO:: 28
The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the forerunners in the technology front, Tirnop continues to lead the way in products and services in India. At Tirnop, all programmers are equal in every respect. They receive identical salaries ans also write code at the same rate.Suppose 12 such programmers take 12 minutes to write 12 lines of code in total. How long will it take 72 programmers to write 72 lines of code in total?
a.6
b.18
c.72
d.12
Ans:12
Similar To quesn no 2::
The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the forerunners in the technology front, Tirnop continues to lead the way in products and services in India. At Tirnop, all programmers are equal in every respect. They receive identical salaries ans also write code at the same rate.Suppose 12 such programmers take 12 minutes to write 12 lines of code in total. How many lines of code can be written by 72 programmers in 72 minutes?
ANS::
12 such programmers take 12 minutes to write 12 lines of code
means
1 programmer take 12 minutes to write 1line
72 programmer take 12 minutes to write 72line in total
72 programmer take 72 minutes to write 432(72*6)line in total
because the time increased into 6 factor(72/6)
or
432
we can by this formula
man*days=work
QUESTION NO::29
For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B, Paul picks A with the same probability as A’s chances of winning. Let’s assume such rumors to be true and that in a match between Ghana and Bolivia, Ghana the stronger team has a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game?
a.4/9
b.2/3
c.1/9
d.5/9
ANS::
(2/3)*(2/3)+(1/3)*(1/3)=5/9
QUESTION NO::30
On planet zorba, a solar blast has melted the ice caps on its equator. 8 years after the ice melts, tiny plantoids called echina start growing on the rocks. echina grows in the form of a circle and the relationship between the diameter of this circle and the age of echina is given by the formula
d = 4 * v (t – 8 ) for t = 8
where d represents the diameter in mm and t the number of years since the solar blast. Jagan recorded the radius of some echina at a particular spot as 8mm. How many years back did the solar blast occur?
a.24
b.12
c.8
d.16
ANS::
d= 4 * v (t – 8 )
in this equation v represents an square root.
d = 4 * sqrt(t-8)
d = 16 as r= 8 given
thus 16 = 4 * sqrt(t-8)
4 = sqrt (t-8)
t-8 = 16
t = 24
QUESTION NO::31
The difference between the ages of two of my three grandchildren is 3. My eldest grandchild is three times older than the age of my youngest grandchild and my eldest grandchild’s age is two years more than the ages of my two youngest grandchildren added together. How old is my eldest grandchild?
a.13
b.10
c.15
d.12
Ans::
15
QUESTION NO::32
A hunter leaves his cabin early in the morning and walks one mile due south. Here he sees a bear and starts chasing it for one mile due east before he is able to shoot the bear. After shooting the bear, he drags it one mile due north back to his cabin where he started that morning. What color is the bear?
a.Brown
b.Black
c.Grey
d.White
Ans::
From North Pole, there are an infinite number of points about 1 mile away , where you can walk 1 mile south, walk one mile east (all the way around the earth back to the same spot), and then back north again,
This is only possible if the cabin of man is at North Pole.
He can walk one mile due south, then one mile due east and finally one mile due north where he finds his cabin again. This means that his cabin can only be at the north pole, and for that reason the bear will be white.
QUESTION NO 33::
One day Rapunzel meets Dwarf and Byte in the Forest of forgetfulness. She knows that Dwarf lies on Mondays, Tuesdays and Wednesdays, and tells the truth on the other days of the week. Byte, on the other hand, lies on Thursdays, Fridays and Saturdays, but tells the truth on the other days of the week. Now they make the following statements to Rapunzel – Dwarf: Yesterday was one of those days when I lie. Byte: Yesterday was one of those days when I lie too. What day is it?
a.Thursday
b.Tuesday
c.Sunday
d.Monday
ANS::
Thursday
Explanation :
On Thursday, Dwarf says truth. i.e Yesterday(Wednesday) was one of those days when I lies. Its true.
On the other hand, On Thursday, Byte lies. i.e Yesterday(Wednesday) was one of those days when I lie too. Its a lie.... So both satisfied. Hence its Thursday.
QUESTION NO 34::
The teacher is testing a student’s proficiency in arithmetic and poses the following question. 1/3 of a number is 3 more than 1/6 of the same number. What is the number? Can you help the student find the answer?
a.12
b.18
c.6
d.21
ANS::
x/3=3+x/6
so,x=18
QUESTION NO 35::
A greengrocer was selling apple at a penny each, chickoos at 2 for a penny and peanuts at 3 for a penny. A father spent 7p and got the same amount of each type of fruit for each of his three children. What did each child get?
a.1 apple, 1 chickoo, 1 peanut
b.1 apple, 2 chickoos, 2 peanuts
c.1 apple, 2 chickoos, 1 peanut
d.1 apple, 3 chickoos, 2 peanuts
ANS::
Go from options
1 apple , 2 chickoos , 1 peanut :::::::::::: 3 children are there so he have to buy 3 apples for dat 3 penny’s. similarly for 2 chickoos each child he have to buy 6 chickoos for dat 3 penny’s and 1 peanut for each child he have to buy 3 peanuts for that 1 penny. So total 7
QUESTION NO:: 36
Here 10 programers, type 10 lines with in 10 minutes then 60lines can type within 60 minutes. How many programmers are needed?
a. 16
b. 6
c. 10
d. 60
ANS::
c.10
QUESTION NO::37
The citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 (in base 8) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?
a. 54
b. 64
c. 265
d. 192
ANS: d
Consider 3 in one's place. The possible numbers are
3,13,23....,73
103,113...,173
.
.
.
703,713...773
i.e 8*8=64 times.
Similarly consider 10's place
70,71,71...77
170,171,...177
.
.
.
770,771...777
Again 8*8=64
Now to hundred's place
700,701...707
.
.
.
770,771,...777
Again 8*8=64
so total 64+64+64=192
QUESTION NO::38
Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, .i.e the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position(.i.e no three points in P lie on a line) is
a.3
b.5
c. 2
d.1
ANS: b
Arrange the points in a circle
QUESTION NO::39
A Hare and a tortoise have a racing along a circle of 100 yards diameter. The tortoise goes in one direction and the Hare in the other. The hare starts after the tortoise has covered 1/5 of its distance and that too leisurely3. A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the. The hare and tortoise meet when the hare has covered only 1/8 of the distance. By what factor should the hare increase its speed so as to tie the race?
a. 37.80
b.8
c. 40
d. 5
QUESTION NO::40
Alice and Bob play the following coins-on-a-stack game. 20 coins are stacked one above the other. One of them is a special (gold) coin and the rest are ordinary coins. The goal is to bring the gold coin to the top by repeatedly moving the topmost coin to another position in the stack. Alice starts and the players take turns. A turn consists of moving the coin on the top to a position i below the top coin (0 = i = 20). We will call this an i-move (thus a 0-move implies doing nothing). The proviso is that an i-move cannot be repeated; for example once a player makes a 2-move, on subsequent turns neither player can make a 2-move. If the gold coin happens to be on top when it's a player's turn then the player wins the game. Initially, the gold coinis the third coin from the top. Then
a. In order to win, Alice's first move should be a 1-move.
b. In order to win, Alice's first move should be a 0-move.
c. In order to win, Alice's first move can be a 0-move or a 1-move.
d. Alice has no winning strategy.
ANS: a
Consider the situation of a 1-move
---C---
---C---
---G---
C represents the normal coin and G the gold coin. So Alice makes a 1-move, which does not have any effect on the arrangement. Next Bob has to make a 0-move or 2-move. If he makes a 0-move, there is no change and if he make a 2-move, the G goes up by one step. If Bob makes a 2-move, then Alice can do a 0-move and win the game. Its difficult to explain the procedure here, contact me if you need a clear answer.
QUESTION NO::41
36 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is
a.12
b.11
c.13
d.18
ANS::
d.12
Understand the question, we have to find the minimum set, so that all other people shake hand to the selected set of people. Let me take an example of 6 people. {a1,a2,a3,a4,a5,a6} Now if we include a minimum set {a2,a5} all other people are shaking hands with them. So if its 2 for 6(1/3rd) then its 36/3=12
QUESTION NO::42
After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?
a.1/12
b.0
c.12/212
d.11/12
ANS:::
b)
Becoz atleast two letter will be inserted in the improper envelop number
QUESTION NO: 45
A hollow cube of size 5cm is taken, with a thickness of 1cm. It is made of smaller cubes of size 1 cm. If 4 faces of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?
a.488
b.500
c.900
d.800
ANS: a
Number of cubes of the solid cube = 5*5*5=125
Number of cubes of the inner cube to make it hollow = 3*3*3=27
Therefore total number of cubes= 125-27=98
98 cubes have a total of 98*6=588 faces.
Now 4 outer surfaces are painted and each face has 5*5 smaller faces. Therefore a total of 5*5*4=100 faces are painted.
Therefore unpainted faces= 588-100=488
QUESTION NO: 46
Planet Fourfi resides in 4-Dimensional space and thus the currency used by its residents are 3-dimensional objects. The rupee notes are cubical in shape while their coins are spherical. However the coin minting machinery lays out some stipulations on the size of the coins.
a.5
b.8
c.6
d.9
ANS : c
Lets start from 64
64 ---1
64+32=96 ---2
96+48=144 ---3
144+72=216--4
216+108=324---5
324+162= 486--6
486+243>512
QUESTION NO: 47
The pacelength P is the distance between the rear of the two consecutive footprints. For men, the formula, n/P=144 gives an approximate relationship between n and P where n=number of steps per minute and P=pacelength in meters. Bernard knows his pacelength is 164cm. The formula applies to Bernard's walking. Calculate Bernard's walking speed in kmph.
a.11.39
b.8.78
c.23.62
d.236.16
QUESTION NO:48
There are two boxes, one containing 10 red balls and the other containing 10 green balls. You are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is
a.14/19
b.37/38
c.1/2
d.3/4
ANS: c
The probability of selecting the box is 1/2 and the probability of selecting the Red ball is 1. So a total of 1/2
QUESTION NO 49::
A man is standing in front of a painting of a man, and he tells us the following: Brothers and sisters have I none, but this man’s father is my father’s son. Who is on the painting?
a.His son
b.His grandfather
c.His father
d.He himself
ANS: a
QUESTION NO :: 50
Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 20, 20 and 30, the number of points equidistant from all the 3 lines is
a.4
b.1
c.3
ANS: b
The Incentre
QUESTION NO:: 51
A lady has fine gloves and hats in her closet- 18 blue, 32 red, and 25 yellow. The lights are out and it is totally dark. In spite of the darkness, she can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each color?
a.50
b.8
c.60
d.42
ANS: 60
There can be lots of logic for this, but approach the simplest one so that we approach to one of the solutions. Suppose the lady first picks 32 Red gloves, and then 24 Yellow gloves. The next pair she pics will be one Yellow and One Blue which does not make a pair. The next two will be blue gloves. So she make a total of 32+24+1+1+2 = 60 picks.
QUESTION NO :: 52
A sheet of paper has statements numbered from 1 to 70. For all values of n from 1 to 70.
Statement n says ' At least n of the statements on this sheet are false.
‘Which statements are true and which are false?
a. The even numbered statements are true and the odd numbered are false.
b. The odd numbered statements are true and the even numbered are false.
c. The first 35 statements are true and the last 35 are false.
d. The first 35 statements are false and the last 35 are false.
ANS: c
Consider 4 statement. First statement say that Atleast 1 is false, and second says atleast 2 is false. If the first two statements are considered as true, it means the Statement 3 and Statement 4 can never be true. Thus out of four, 2 are false. This pattern continues and can be concluded as the result.
QUESTION NO:: 53
Ramu & Sangeeta went for biological analysis to a island which is 34km from their place. They travelled in a boat which went at a speed of 2m/s. when they are in half a distance in the boat sangeeta note there are 7 leg & 8 leg octopuses under the water. Ramu counted the total number of legs of octopuses and got 54. Sangeetha instantly said I know how many 7 leged octopuses are there under the water. They both reached the island after 20 min they left . How many seven leged octopuses does sangeetha calculate?
a. 4
b. 5
c. 6
d. 7
ANS: The options provided are wrong. The answer is 2.
7(X)+8(Y)=54 -- X : no of 7 legged octopus. Y: no of 8 legged octopus. Try substituting values of X and you have to get an integer value for Y.
QUESTION NO:: 54
There are 14 spots. Each spot has 8 seats. 28 people seated in all the spots. No similar number people sat in any spot. How many spots left with no people at all.
a. 5
b. 6
c. 7
d. 8
ANS: c
Same logic as explained in Qn. 58
QUESTION NO:: 55
Susan made a block with small cubes of 8 cubic cm volume to make a block 3 small cubes long, 9 small cubes wide and 5 small cubes deep. She realizes that she has used more small cubes than she really needed. She realized that she could have glued a fewer number of cubes together to lock like a block with same dimensions, if it were made hollow. What is the minimum number of cubes that she needs to make the block?
a. 114
b. 135
c. 21
d. 71
ANS: a
Total number of cubes required to make the solid cube = 3*9*5
To make it hollow, we can remove an inner cube, which has 1*7*3 cubes.
So total number of cubes= 3*9*5-1*7*3=114
QUESTION NO:: 56
In the year 2002, Britain was reported to have had 4.3m closed – circuit television (CCTV)
cameras – one for every 14 people in the country . This scrutiny is supposed to deter and detect crime. In one criminal case, the police interrogates two suspects . The ratio between the ages of the two suspects is 6:5 and the sum of their ages is 6:5 and the sum of their ages is 55 years. After how many years will the ratio be 8:7.?
a. 11
b. 6
c. 10
d. 5
QUESTION NO::57
Francois Pachet , a researcher at Sony Computer Science laboratories is also a jazz musician. He decided to build a robot able to improvise like a pro. Named Continuator, the robot can duet with a live musician in real- time. It listens to a musical phrase and then computes a complementary phrase with the same playing style. If the cost of making the robot is divided between materials , labour and overheads in the ratio of 4:6:2.If the materials cost $108. the cost of the robot is
a. $270
b. $324
c. $216
d. $ 648
ANS: b.
4 is 1/3rd of 12(4+6+2). So you have the answer as 108*3.
QUESTION NO:: 58
In the reading room of a library, there are23 reading spots. Each reading spot consists of a round table with 9 chairs placed around it. There are some readers such that in each occupied reading spot there are different numbers of readers. If in all there are 36 readers, how many reading spots do not have even a single reader?
a. 8
b. None
c. 16
d 15
ANS: d
The posts should have different numbers -- 1+2+3+4+5+6+7+8=36
Therefore 8 Posts are filled, implies 23-8=15 Unfilled.
Rearrange the following letters to make a word and choose the category in which it fits.
RAPETEKA
a. city
b. fruit
c. bird
d. vegetable
Correct answer: bird (parakeet)
QUESTION NO 2::
A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the hare in the other. The hare starts after the tortoise has covered 1/5 of its distance and that too leisurely. The hare and tortoise meet when the hare has covered only 1/8 of the distance. By what factor should the hare increase its speed so as to tie the race?
a. 8
b. 37.80
c. 5
d. 40
ANS :37.80
QUESTION NO 3::
There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one litre every hour in A, it gets filled up like 10, 20, 40, 80, 160... in tank B. (At the end of first hour, B has 10 litres , second hour it has 20, and so on). If tank B is 1/32 filled after 21 hours, what is the total duration required to fill it completely?
a. 26 hrs
b. 25 hrs
c. 5 hrs
d. 27 hrs
ANS:26 hrs
A similar question with numbers changed --
There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one litre every hour in A, it gets filled up like 10, 20, 40, 80, 160... in tank B. (At the end of first hour, B has 10 litres , second hour it has 20, and so on). If tank B is 1/32 filled after 3 hours, what is the total duration required to fill it completely?
a. 8 hrs
b. 9 hrs
c. 10 hrs
d. 7 hrs
QUESTION NO 4::
Anoop managed to draw 7 circles of equal radii with their centres on the diagonal of a square such that the two extreme circles touch two sides of the square and each middle circle touches two circles on either side. Find the ratio of the radius of the circles to the side of the square.
a. (2+ 7√2):1
b. 1:(2+ 6√2)
c. 1:(4+ 7√3)
d. 1:(2+ 7√2)
ANS: b
QUESTION NO 5:
A sheet of paper has statements numbered from 1 to 30. For all values of n from 1 to 30, statement n says "At most n of the statements on this sheet are false". Which statements are true and which are false?
a. The even numbered statements are true and the odd numbered are false.
b. All statements are false.
c. All statements are true.
d. The odd numbered statements are true and the even numbered are false.
ANS: b
QUESTION NO 6::
Ferrari S.p.A. is an Italian sports car manufacturer based in Maranello, Italy. Founded by Enzo Ferrari in 1928 as Scuderia Ferrari, the company sponsored drivers and manufactured race cars before moving into production of street-legal vehicles in 1947 as Ferrari S.p.A.. Throughout its history, the company has been noted for its continued participation in racing, especially in Formula One, where it has enjoyed great success. Rohit once bought a Ferrari. It could go 2 times as fast as Mohit's old Mercedes. If the speed of Mohit's Mercedes is 32 km/hr and the distance travelled by the Ferrari is 952 km, find the total time taken in hours for Rohit to drive that distance.
a. 29.75
b. 14.88
c. 15.88
d. 476
ANS: b
QUESTION NO 7::
On the planet Oz, there are 8 days in a week- Sunday to Saturday and another day called Oz day. There are 36 hours in a day and each hour has 90 min while each minute has 60 sec. As on earth, the hour hand covers the dial twice every day.
Find the approximate angle between the hands of a clock on Oz when the time is 12:40 am.
a. 251
b.111
c.71
d.89
ANS: d
QUESTION NO :: 8
For the FIFA world cup. Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B,Paul picks A with the same probability as A’s chance of winning. Let’s assume such rumors to be true and than in match between Ghana and Bolivia, Ghana the stronger team has a probability of 2/3 of winning the game.
What is the probability that paul will correctly pick the winner of the Ghana-Bollivia game ?
a.5/9
b.4/9
c.1/9
d.2/3
ANS : a
QUESTION NO::9
Alok and Bhanu play the following min-max game. Given the expression N = 9 +X + Y– Z where X, Y and Z are variables representing single digits (0 to 9), Alok would like to maximize N while Bhanu
would like to minimize it. Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X, Y or Z). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the value for the remaining variable. Assuming both play to their optimal
strategies, the value of N at the end of the game would be
a. 27
b. 18
c. 20
d. 0.0
ANS: b
QUESTION NO::10
Alok and Bhanu play the following min-max game. Given the expression N = X– Y – Z where X, Y and Z are variables representing single digits (0 to 9), Alok would like to maximize N while Bhanu would like to minimize it. Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X, Y or Z). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the value for the remaining variable. Assuming both play to their optimal strategies, the value of N at the end of the game would be
a. 2
b. 4
c. 9
d. -18
QUESTION NO::11
Alok and Bhanu play the following min-max game. Given the expression N = 38 + X*(Y – Z) where X, Y and Z are variables representing single digits (0 to 9), Alok would like to maximize N while Bhanu would like to minimize it. Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X, Y or Z). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the value for the remaining variable. Assuming both play to their optimal strategies, the value of N at the end of the game would be
a.38
b.119
Similar question with numbers changed --
Alok and Bhanu play the following min-max game. Given the expression N = 12 + X*(Y – Z) where X, Y and Z are variables representing single digits (0 to 9), Alok would like to maximize N while Bhanu would like to minimize it. Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X, Y or Z). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the value for the remaining variable. Assuming both play to their optimal strategies, the value of N at the end of the game would be
a.93
b.12
c.-69d.30
QUESTION NO::12
A person drives with constant speed and after some time he sees a milestone with 2 digits. Then travels for 1 hours and sees the same 2 digits in reverse order. 1 hours later he sees that the milestone has the same 2 digits with a 0 between them. What is the speed of the car?
a.54.00 mph
b.45.00 mph
c.27.00 mph
d.36.00 mph
ANS: b
s=speed
"Then travels for 1 hour and sees the same 2 digits in reverse order."
10x + y + 1s = 10y + x
10x - x + s = 10y - y
9x + s = 9y
1 hours later he sees that the milestone has the same 2 digits with a 0 between them."
10y + x + s = 100x + y
10y - y + s = 100x - x
9y + s = 99x
Rearrange the above two equations for elimination
9x - 9y + s = 0
-99x+9y + s = 0
----------------adding eliminates y
-90x + 2s = 0
2s = 90x
s = 45x
x has to equal 1, then s = 45 mph (If x=2 and s=90 mph, when added to
a two digit milestone, could not be at another two digit milestone.)
QUESTION NO::13
Fermat’s Last Theorem is a statement in number theory which states that it is impossible to separate any power higher than the second into two like powers, or, more precisely- If an integer n is greater than 2, then the equation a^n b^n = c^n has no solutions in non-zero integers a, b, and c. Now, if the difference of any two numbers is 9 and their product is 17, what is the sum of their squares?
a.43
b.45
c.98
d.115
ANS: d
QUESTION NO::14
India with a burgeoning population and a plethora of vehicles (at last count there were more than 20 million of them) has witnessed big traffic jams at all major cities. Children often hone their counting skills by adding the wheels of vehicles in schoolyards or bus depots and guessing the number of vehicles.
Alok, one such child, finds only bicycles and 4 wheeled wagons in his schoolyard. He counts the totalnumber of wheels to be 46. What could be the possible number of bicycles?
a.25
b.5
c.4
ANS: b
QUESTION NO::15
Alchemy is an occult tradition that arose in the ancient Persian empire. Zosimos of Panopolis was an early alchemist. Zara, reads about Zosimos and decides to try some experiments. One day, she collects two buckets, the first containing one litre of ink and the second containing one litre of cola. Suppose she takes one cup of ink out of the first bucket and pours it into the second bucket. After mixing she takes one cup of the mixture from the second bucket and pours it back into the first bucket. Which one of the following statements holds now?
a.There is more cola in the first bucket than ink in the second bucket.
b.There is as much cola in the first bucket as there is ink in the second bucket.
c.There is less cola in the first bucket than ink in the second bucket.
ANS:c
QUESTION NO:: 16
Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line; i.e. the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The maximum value of n1(P) over all configurations P of 19 points in the plane is
a.10
b.9
c.3
d.5
ANS : The options given are wrong, the answer would be 19. Or it can be taken as the maximum value, making a. here.
QUESTION NO :: 17
15 suspects are rounded by the police and questioned about a bank robbery. Only one of them is guilty. The suspects are made to stand in a line and each person declares that the person next to him on his right is guilty. The rightmost person is not questioned. Which of the following possibilities are true?
A. All the suspects are lying or leftmost is innocent
B. All the suspects are lying and leftmost is innocent
a.A only
b.B only
c.A and B
d.Neither A and B
ANS : a
Considering that all are lying that "The one to my right is guilty" literally means than 2-15 are innocent. If they are all lying, leftmost should be guilty.
QUESTION NO::18
Alchemy is an occult tradition that arose in the ancient Persian empire. Zosimos of Panopolis was an early alchemist. Zara, reads about Zosimos and decides to try some experiments. One day, she collects two buckets, the first containing one litre of ink and the second containing one litre of cola. Suppose she takes one cup of ink out of the first bucket and pours it into the second bucket. After mixing she takes one cup of the mixture from the second bucket and pours it back into the first bucket. Which one of the following statements holds now?
a.There is more cola in the first bucket than ink in the second bucket.
b.There is as much cola in the first bucket as there is ink in the second bucket.
c.There is less cola in the first bucket than ink in the second bucket.
ANS: c
QUESTION NO ::19
Both A and B Alice and Bob play the following chip-off-the-table game. Given a pile of 58 chips, Alice first picks at least one chip but not all the chips. In subsequent turns, a player picks at least one chip but no more than the number picked on the previous turn by the opponent. The player to pick the last chip wins. Which of the following is true?
a.In order to win, Alice should pick 14 chips on her first turn.
b.In order to win, Alice should pick two chips on her first turn.
c.In order to win, Alice should pick one chip on her first turn.
QUESTION NO ::20
30 teams enter a hockey tournament. A team is out of the tournament if it loses 2 games. What is the maximum number of games to be played to decide one winner?
a.60
b.59
c.61
d.30
e.34
ANS: b
29 teams have to fail two games, so 29*2=58, the winner loses one game. Therefore 58+1=59.
QUESTION NO::21
Suppose 12 monkeys take 12 minutes to eat 12 bananas. How many monkeys would it take to eat 72 bananas in 72 minutes?
a.6
b.72
c.12
ANS: c
QUESTION NO::22
Alok is attending a workshop “How to do more with less” and today’s theme is Working with fewer digits . The speakers discuss how a lot of miraculous mathematics can be achieved if mankind (as well as
womankind) had only worked with fewer digits. The problem posed at the end of the workshop is How many 5 digit numbers can be formed using the digits 1, 2, 3, 4, 5 (but with repetition) that are divisible by 4? Can you help Alok find the answer?
a.625
b.375
c.230
d.500
ANS: a
QUESTION NO::23
A and B play a game of dice between them. The dice consist of colors on their faces (instead of numbers). When the dice are thrown, A wins if both show the same color; otherwise B wins. One die has 4 red face and 2 blue faces. How many red and blue faces should the other die have if the both players have the same chances of winning?
a.3 red and 3 blue faces
b.2 red and remaining blue
c.6 red and 0 blue
d.4 red and remaining blue
ANS: a
QUESTION NO::24
A sheet of paper has statements numbered from 1 to 45. For all values of n from 1 to 45, statement n says “At most n of the statements on this sheet are false”. Which statements are true and which are false?
a.The odd numbered statements are true and the even numbered are false.
b.The even numbered statements are true and the odd numbered are false.
c.All statements are false.
QUESTION NO:: 25
All statemeThere are two containers A and B. A is half filled with wine whereas B which is 3 times the size of A contains one quarter portion wine. If both containers are filled with water and the contents are poured into container C, what portion of container C is wine?
a. .30
b. .31
c. .42
d. .25
QUESTION NO:: 25
A and B play a game of dice between them. The dice consist of colors on their faces (instead of numbers). When the dice are thrown, A wins if both show the same color; otherwise B wins. One die has 3 red faces and 3 blue faces. How many red and blue faces should the other die have if the both players have the same chances of winning?
a.5 red and 1 blue faces
b.1 red and 5 blue faces
c.3 red and 3 blue faces
QUESTION NO:: 27
A circular dartboard of radius 1 foot is at a distance of 20 feet from you. You throw a dart at it and it hits the dartboard at some point Q in the circle. What is the probability that Q is closer to the center of the circle than the periphery?
a.0.75
b.1
c.0.5
d.0.25
Ans:.25
Here the data about the distance is of no use.
For radius of 1 m if dart is inside the circle of 1/2 m radius the dart is closer to center than periphery
so area of 1/2 m circle is pie/4
area of board is pie
So probability = 0.25
QUESTION NO:: 28
The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the forerunners in the technology front, Tirnop continues to lead the way in products and services in India. At Tirnop, all programmers are equal in every respect. They receive identical salaries ans also write code at the same rate.Suppose 12 such programmers take 12 minutes to write 12 lines of code in total. How long will it take 72 programmers to write 72 lines of code in total?
a.6
b.18
c.72
d.12
Ans:12
Similar To quesn no 2::
The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the forerunners in the technology front, Tirnop continues to lead the way in products and services in India. At Tirnop, all programmers are equal in every respect. They receive identical salaries ans also write code at the same rate.Suppose 12 such programmers take 12 minutes to write 12 lines of code in total. How many lines of code can be written by 72 programmers in 72 minutes?
ANS::
12 such programmers take 12 minutes to write 12 lines of code
means
1 programmer take 12 minutes to write 1line
72 programmer take 12 minutes to write 72line in total
72 programmer take 72 minutes to write 432(72*6)line in total
because the time increased into 6 factor(72/6)
or
432
we can by this formula
man*days=work
QUESTION NO::29
For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B, Paul picks A with the same probability as A’s chances of winning. Let’s assume such rumors to be true and that in a match between Ghana and Bolivia, Ghana the stronger team has a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game?
a.4/9
b.2/3
c.1/9
d.5/9
ANS::
(2/3)*(2/3)+(1/3)*(1/3)=5/9
QUESTION NO::30
On planet zorba, a solar blast has melted the ice caps on its equator. 8 years after the ice melts, tiny plantoids called echina start growing on the rocks. echina grows in the form of a circle and the relationship between the diameter of this circle and the age of echina is given by the formula
d = 4 * v (t – 8 ) for t = 8
where d represents the diameter in mm and t the number of years since the solar blast. Jagan recorded the radius of some echina at a particular spot as 8mm. How many years back did the solar blast occur?
a.24
b.12
c.8
d.16
ANS::
d= 4 * v (t – 8 )
in this equation v represents an square root.
d = 4 * sqrt(t-8)
d = 16 as r= 8 given
thus 16 = 4 * sqrt(t-8)
4 = sqrt (t-8)
t-8 = 16
t = 24
QUESTION NO::31
The difference between the ages of two of my three grandchildren is 3. My eldest grandchild is three times older than the age of my youngest grandchild and my eldest grandchild’s age is two years more than the ages of my two youngest grandchildren added together. How old is my eldest grandchild?
a.13
b.10
c.15
d.12
Ans::
15
QUESTION NO::32
A hunter leaves his cabin early in the morning and walks one mile due south. Here he sees a bear and starts chasing it for one mile due east before he is able to shoot the bear. After shooting the bear, he drags it one mile due north back to his cabin where he started that morning. What color is the bear?
a.Brown
b.Black
c.Grey
d.White
Ans::
From North Pole, there are an infinite number of points about 1 mile away , where you can walk 1 mile south, walk one mile east (all the way around the earth back to the same spot), and then back north again,
This is only possible if the cabin of man is at North Pole.
He can walk one mile due south, then one mile due east and finally one mile due north where he finds his cabin again. This means that his cabin can only be at the north pole, and for that reason the bear will be white.
QUESTION NO 33::
One day Rapunzel meets Dwarf and Byte in the Forest of forgetfulness. She knows that Dwarf lies on Mondays, Tuesdays and Wednesdays, and tells the truth on the other days of the week. Byte, on the other hand, lies on Thursdays, Fridays and Saturdays, but tells the truth on the other days of the week. Now they make the following statements to Rapunzel – Dwarf: Yesterday was one of those days when I lie. Byte: Yesterday was one of those days when I lie too. What day is it?
a.Thursday
b.Tuesday
c.Sunday
d.Monday
ANS::
Thursday
Explanation :
On Thursday, Dwarf says truth. i.e Yesterday(Wednesday) was one of those days when I lies. Its true.
On the other hand, On Thursday, Byte lies. i.e Yesterday(Wednesday) was one of those days when I lie too. Its a lie.... So both satisfied. Hence its Thursday.
QUESTION NO 34::
The teacher is testing a student’s proficiency in arithmetic and poses the following question. 1/3 of a number is 3 more than 1/6 of the same number. What is the number? Can you help the student find the answer?
a.12
b.18
c.6
d.21
ANS::
x/3=3+x/6
so,x=18
QUESTION NO 35::
A greengrocer was selling apple at a penny each, chickoos at 2 for a penny and peanuts at 3 for a penny. A father spent 7p and got the same amount of each type of fruit for each of his three children. What did each child get?
a.1 apple, 1 chickoo, 1 peanut
b.1 apple, 2 chickoos, 2 peanuts
c.1 apple, 2 chickoos, 1 peanut
d.1 apple, 3 chickoos, 2 peanuts
ANS::
Go from options
1 apple , 2 chickoos , 1 peanut :::::::::::: 3 children are there so he have to buy 3 apples for dat 3 penny’s. similarly for 2 chickoos each child he have to buy 6 chickoos for dat 3 penny’s and 1 peanut for each child he have to buy 3 peanuts for that 1 penny. So total 7
QUESTION NO:: 36
Here 10 programers, type 10 lines with in 10 minutes then 60lines can type within 60 minutes. How many programmers are needed?
a. 16
b. 6
c. 10
d. 60
ANS::
c.10
QUESTION NO::37
The citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 (in base 8) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?
a. 54
b. 64
c. 265
d. 192
ANS: d
Consider 3 in one's place. The possible numbers are
3,13,23....,73
103,113...,173
.
.
.
703,713...773
i.e 8*8=64 times.
Similarly consider 10's place
70,71,71...77
170,171,...177
.
.
.
770,771...777
Again 8*8=64
Now to hundred's place
700,701...707
.
.
.
770,771,...777
Again 8*8=64
so total 64+64+64=192
QUESTION NO::38
Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, .i.e the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position(.i.e no three points in P lie on a line) is
a.3
b.5
c. 2
d.1
ANS: b
Arrange the points in a circle
QUESTION NO::39
A Hare and a tortoise have a racing along a circle of 100 yards diameter. The tortoise goes in one direction and the Hare in the other. The hare starts after the tortoise has covered 1/5 of its distance and that too leisurely3. A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the. The hare and tortoise meet when the hare has covered only 1/8 of the distance. By what factor should the hare increase its speed so as to tie the race?
a. 37.80
b.8
c. 40
d. 5
QUESTION NO::40
Alice and Bob play the following coins-on-a-stack game. 20 coins are stacked one above the other. One of them is a special (gold) coin and the rest are ordinary coins. The goal is to bring the gold coin to the top by repeatedly moving the topmost coin to another position in the stack. Alice starts and the players take turns. A turn consists of moving the coin on the top to a position i below the top coin (0 = i = 20). We will call this an i-move (thus a 0-move implies doing nothing). The proviso is that an i-move cannot be repeated; for example once a player makes a 2-move, on subsequent turns neither player can make a 2-move. If the gold coin happens to be on top when it's a player's turn then the player wins the game. Initially, the gold coinis the third coin from the top. Then
a. In order to win, Alice's first move should be a 1-move.
b. In order to win, Alice's first move should be a 0-move.
c. In order to win, Alice's first move can be a 0-move or a 1-move.
d. Alice has no winning strategy.
ANS: a
Consider the situation of a 1-move
---C---
---C---
---G---
C represents the normal coin and G the gold coin. So Alice makes a 1-move, which does not have any effect on the arrangement. Next Bob has to make a 0-move or 2-move. If he makes a 0-move, there is no change and if he make a 2-move, the G goes up by one step. If Bob makes a 2-move, then Alice can do a 0-move and win the game. Its difficult to explain the procedure here, contact me if you need a clear answer.
QUESTION NO::41
36 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is
a.12
b.11
c.13
d.18
ANS::
d.12
Understand the question, we have to find the minimum set, so that all other people shake hand to the selected set of people. Let me take an example of 6 people. {a1,a2,a3,a4,a5,a6} Now if we include a minimum set {a2,a5} all other people are shaking hands with them. So if its 2 for 6(1/3rd) then its 36/3=12
QUESTION NO::42
After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?
a.1/12
b.0
c.12/212
d.11/12
ANS:::
b)
Becoz atleast two letter will be inserted in the improper envelop number
QUESTION NO::43
There is a toy train that can make 10 musical sounds. It makes 2 musical sounds after being defective. What is the probability that same musical sound would be produced 5 times consecutively? (1 of )?
QUESTION NO::44
By using 1,2,3,4,5, how many 12 digit no. can be formed which is divisible by 4, repetation of no. is allowed?
QUESTION NO: 45
A hollow cube of size 5cm is taken, with a thickness of 1cm. It is made of smaller cubes of size 1 cm. If 4 faces of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?
a.488
b.500
c.900
d.800
ANS: a
Number of cubes of the solid cube = 5*5*5=125
Number of cubes of the inner cube to make it hollow = 3*3*3=27
Therefore total number of cubes= 125-27=98
98 cubes have a total of 98*6=588 faces.
Now 4 outer surfaces are painted and each face has 5*5 smaller faces. Therefore a total of 5*5*4=100 faces are painted.
Therefore unpainted faces= 588-100=488
QUESTION NO: 46
- The diameter of the coins should be at least 64mm and not exceed 512 mm.
- Given a coin, the diameter of the next larger coin is at least 50% greater.
- The diameter of the coin must always be an integer.
a.5
b.8
c.6
d.9
ANS : c
Lets start from 64
64 ---1
64+32=96 ---2
96+48=144 ---3
144+72=216--4
216+108=324---5
324+162= 486--6
486+243>512
QUESTION NO: 47
The pacelength P is the distance between the rear of the two consecutive footprints. For men, the formula, n/P=144 gives an approximate relationship between n and P where n=number of steps per minute and P=pacelength in meters. Bernard knows his pacelength is 164cm. The formula applies to Bernard's walking. Calculate Bernard's walking speed in kmph.
a.11.39
b.8.78
c.23.62
d.236.16
QUESTION NO:48
There are two boxes, one containing 10 red balls and the other containing 10 green balls. You are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is
a.14/19
b.37/38
c.1/2
d.3/4
ANS: c
The probability of selecting the box is 1/2 and the probability of selecting the Red ball is 1. So a total of 1/2
QUESTION NO 49::
A man is standing in front of a painting of a man, and he tells us the following: Brothers and sisters have I none, but this man’s father is my father’s son. Who is on the painting?
a.His son
b.His grandfather
c.His father
d.He himself
ANS: a
QUESTION NO :: 50
Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 20, 20 and 30, the number of points equidistant from all the 3 lines is
a.4
b.1
c.3
ANS: b
The Incentre
QUESTION NO:: 51
A lady has fine gloves and hats in her closet- 18 blue, 32 red, and 25 yellow. The lights are out and it is totally dark. In spite of the darkness, she can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each color?
a.50
b.8
c.60
d.42
ANS: 60
There can be lots of logic for this, but approach the simplest one so that we approach to one of the solutions. Suppose the lady first picks 32 Red gloves, and then 24 Yellow gloves. The next pair she pics will be one Yellow and One Blue which does not make a pair. The next two will be blue gloves. So she make a total of 32+24+1+1+2 = 60 picks.
QUESTION NO :: 52
A sheet of paper has statements numbered from 1 to 70. For all values of n from 1 to 70.
Statement n says ' At least n of the statements on this sheet are false.
‘Which statements are true and which are false?
a. The even numbered statements are true and the odd numbered are false.
b. The odd numbered statements are true and the even numbered are false.
c. The first 35 statements are true and the last 35 are false.
d. The first 35 statements are false and the last 35 are false.
ANS: c
Consider 4 statement. First statement say that Atleast 1 is false, and second says atleast 2 is false. If the first two statements are considered as true, it means the Statement 3 and Statement 4 can never be true. Thus out of four, 2 are false. This pattern continues and can be concluded as the result.
QUESTION NO:: 53
Ramu & Sangeeta went for biological analysis to a island which is 34km from their place. They travelled in a boat which went at a speed of 2m/s. when they are in half a distance in the boat sangeeta note there are 7 leg & 8 leg octopuses under the water. Ramu counted the total number of legs of octopuses and got 54. Sangeetha instantly said I know how many 7 leged octopuses are there under the water. They both reached the island after 20 min they left . How many seven leged octopuses does sangeetha calculate?
a. 4
b. 5
c. 6
d. 7
ANS: The options provided are wrong. The answer is 2.
7(X)+8(Y)=54 -- X : no of 7 legged octopus. Y: no of 8 legged octopus. Try substituting values of X and you have to get an integer value for Y.
QUESTION NO:: 54
There are 14 spots. Each spot has 8 seats. 28 people seated in all the spots. No similar number people sat in any spot. How many spots left with no people at all.
a. 5
b. 6
c. 7
d. 8
ANS: c
Same logic as explained in Qn. 58
QUESTION NO:: 55
Susan made a block with small cubes of 8 cubic cm volume to make a block 3 small cubes long, 9 small cubes wide and 5 small cubes deep. She realizes that she has used more small cubes than she really needed. She realized that she could have glued a fewer number of cubes together to lock like a block with same dimensions, if it were made hollow. What is the minimum number of cubes that she needs to make the block?
a. 114
b. 135
c. 21
d. 71
ANS: a
Total number of cubes required to make the solid cube = 3*9*5
To make it hollow, we can remove an inner cube, which has 1*7*3 cubes.
So total number of cubes= 3*9*5-1*7*3=114
QUESTION NO:: 56
In the year 2002, Britain was reported to have had 4.3m closed – circuit television (CCTV)
cameras – one for every 14 people in the country . This scrutiny is supposed to deter and detect crime. In one criminal case, the police interrogates two suspects . The ratio between the ages of the two suspects is 6:5 and the sum of their ages is 6:5 and the sum of their ages is 55 years. After how many years will the ratio be 8:7.?
a. 11
b. 6
c. 10
d. 5
QUESTION NO::57
Francois Pachet , a researcher at Sony Computer Science laboratories is also a jazz musician. He decided to build a robot able to improvise like a pro. Named Continuator, the robot can duet with a live musician in real- time. It listens to a musical phrase and then computes a complementary phrase with the same playing style. If the cost of making the robot is divided between materials , labour and overheads in the ratio of 4:6:2.If the materials cost $108. the cost of the robot is
a. $270
b. $324
c. $216
d. $ 648
ANS: b.
4 is 1/3rd of 12(4+6+2). So you have the answer as 108*3.
QUESTION NO:: 58
In the reading room of a library, there are23 reading spots. Each reading spot consists of a round table with 9 chairs placed around it. There are some readers such that in each occupied reading spot there are different numbers of readers. If in all there are 36 readers, how many reading spots do not have even a single reader?
a. 8
b. None
c. 16
d 15
ANS: d
The posts should have different numbers -- 1+2+3+4+5+6+7+8=36
Therefore 8 Posts are filled, implies 23-8=15 Unfilled.
Aptitude Questions 2011
(1)
A sheet of paper has statements numbered from 1 to 70. For all values of n from 1 to 70. Statement n says ‘At least n of the statements on this sheet are false.’ Which statements are true and which are false?
(a) The even numbered statements are true and the odd numbered are false.
(b) The odd numbered statements are true and the even numbered are false.
(c) The first 35 statements are true and the last 35 are false.
(d) The first 35 statements are false and the last 35 are false.
(2)
Unnecessary data. A lady has fine gloves and hats in her closet- 18 blue- 32 red , 10 white , 25 yellow, 55 purple, 30 orange. The lights are out and it is totally dark in spite of the darkness. She can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each color of blue, red, yellow?
(a) 59
(b) 8
(c) 50
(d) 42
(3)
Which of the following is not permitted under the
rules as stated.
(A) A brown male marrying his father’s sister
(B) A red female marrying her mother’s brother
(C) A widower marrying his wife’s sister
(D) A widow marrying her divorced daughter’s
ex-husband
(4)
How many four digit numbers can be formed using the digits 1, 2, 3, 4, 5 (but with repetition) that are divisible by 4? Can you help Alok find the answer?
(a) 100
(b) 125
(c) 75
(d) 85
(5)
If “PROMPT” is coded as QSPLOS ,then “PLAYER” should be
(a) QMBZFS
(b) QWMFDW
(c) QUREXM
(d) URESTI
(1)
Ans: c
Sol:
70/2=35.hence first half 35 are true and second half 35 are false
Note
For this type of Questions, follow this tricks:
(i)At least first half are true, Last half are false
(ii)Exactly- Last second one is true or (N-1)th Statement is true
(iii)Almost- All are true.
(2)
Ans: a
Sol:
(32+25+2)
Note:
For this type of questions , use this formula:
(i)Bigger+Middle+1 (Suppose 18, 32, 25 =32+25+1)
(ii) If you do not find answer in options, choose the one closer those the answer you got.
(3)
Ans:b
(4)
Ans: b
Sol:
5^n-1= 5^4-1=125, n= no of digits
(5)
Sol:
PROMPT=QSPLOS
(P=Q)&(R=S).Hence starting and ending should beQ and S respectively
Therefore,PLAYER=QMBZFS
Latest TCS Fresher Job Interview Paper Pattern : 24th-August-2011
1. (1/3) of a number is 3 more than the (1/6) of the same number?
a) 6
b)16
c)18
d)21
Ans: 18
2. There are two water tanks A and B, A is much smaller than B. While water fills at the rate
of 1 liter every hour in A, it gets filled up like, 10, 20, 40, 80, 160 in tank B. (At the end of
first hour, B has 10 liters, second hour it has 20 liters and so on). If tank B is 1/4 filled of the
10 hours, what is total duration of hours required to fill it completely?
a) 12
b) 25
c) 05
d) 27
Ans: 12
3. Samita was making a cube with dimensions 5*5*5 using 1*1*1 cubes. What is the number
of cubes needed to make a hollow cube looking of the same shape? If we are painting only 2
face of each cube then how many faces will remain unpaint???
a) 98
b) 104
c) 538
d) 650
Ans: 538
Sol: (5*5*5-3*3*3)=125-27=98*no of faces=98*6=588-(no of sides painted)=588-50=538
4. Middle- earth is a fictional land inhabited by hobbits, elves, dwarves and men. The hobbits
and elves are peaceful creatures that prefer slow, silent lives and appreciate nature and art.
The dwarves and the men engage in physical games. The game is as follows. A tournament is
one where out of the two teams that play a match, the one that loses get eliminated. The
matches are played in different rounds, where in every round; half of the teams get eliminated
from the tournament. If there are 8 rounds played in knock out tournament, how many
matches were played?
a) 257
b) 256
c) 72
d) 255
Ans: 255
Sol: 2^n-1=2^8-1=255
5. Mr. bean having magical balls 25 pink, 10 green, 31 red, 31 yellow, 30 purple. He
drenched in rain red, green, and yellow turn into white what is the maximum probability of a
pair of same color ?
Ans : 31+31+ 2(worst case probability)= 64
6. There is 22 friends (A1, A2, A3....A22).If A1 have to have shake with all without repeat.
How many handshakes possible?
a) 6
b) 21
c) 28
d) 7
Ans: 21 since cycle will not form.
7. we are having 54 men doing hand shake in set what will be minimum required hand shakes
for minimum 1 hand shake?
Ans : {1,2,3,4,5,6,…..54}
Set= { 2,5,8,………..53}
So1 set will be ans 18
8. On planet korba, a solar blast has melted the ice caps on its equator. 9 years after the ice
melts, tiny planetoids called echina start growing on the rocks. Echina grows in the form of
circle, and the relationship between the diameter of this circle and the age of echina is given
by the formula d = 4*v (t-9) for t = 9 where d represents the diameter in mm and t the number
of years since the solar blast. Jagan recorded the radius of some echina at a particular spot as
7mm. How many years back did the solar blast occur?
a) 17
b) 21.25
c) 12.25
d) 14.05
9. Ferrari S.P.A is an Italian sports car manufacturer based in Maranello, Italy. Founded by
Enzo Ferrari in 1928 as Scuderia Ferrari, the company sponsored drivers and manufactured
race cars before moving into production of street-legal vehicles in 1947 as Ferrari S.P.A.
Throughout its history, the company has been noted for its continued participation in racing,
especially in Formula One where it has employed great success .Rohit once bought a Ferrari.
It could go 4 times as fast as Mohan's old Mercedes. If the speed of Mohan's Mercedes is 35
km/hr and the distance traveled by the Ferrari is 490 km, find the total time taken for Rohit to
drive that distance.
a) 20.72
b) 3.5
c) 238.25
d) 6.18
10. A sheet of paper has statements numbered from 1 to 70. For all values of n from 1 to 70.
Statement n says ' At least n of the statements on this sheet are false. ‘Which statements are
true and which are false?
a) The even numbered statements are true and the odd numbered are false.
b) The odd numbered statements are true and the even numbered are false.
c) The first 35 statements are true and the last 35 are false.
d) The first 35 statements are false and the last 35 are false.
Sol: when
Rule 1: exact ( n-1)th will be true and other will be false
Rule2: At least (first half will be true)
Rule 3: At most (all true)
Example : exactly 40 statement 39th will be true other than it false
11. If there are 254 barrels out of them one is poisoned if a person tastes very little he will die
within 14 hours so if there are mice to test and 24 hours to test, how many mices are required
to find the poisoned can?
a) 3
b) 2
c) 6
d) 8
Ans : 2^n > no of barrels
Then n=will be required mice N=8
12. Consider two tumblers, the first containing Water and next contains coffee. Suppose you
take one spoon of water out of the first tumbler and pour it into the second tumbler. After
moving you take one spoon of the mixture from the second tumbler and pour it back into the
first tumbler . Which one of the following statement holds now?
a) There is less coffee in the first tumbler than water in the second tumblers
b) There is more coffee in the firs tumbler than water in the second tumbler
c) There is as much coffee in the first tumbler as there is water in the second tumbler
d) None of the statements holds true
Ans: both will be equal
13. Given a collection of points P in the plane, a 1-set is a point in P that can be separated
from the rest by a line, that is the point lies on one side of the line while the others lie on the
other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over
all configurations P of 5 points in the plane in general position (that is no three points in P lie
on a line) is
a)3
b)5
c) 2
d)1
Ans: 5 same as given no of points
14. The citizens of planet nigiet are 8 fingered and have thus developed their decimal system
in base 8. A certain street in nigiet contains 1000 (in base 8) buildings numbered 1 to 1000.
How many 3s are used in numbering these buildings?
a) 54
b) 64
c) 265
d) 192
Ans: 192
Some times base value is change like: 9finger, 1 to 100(base 9)
For 1..100 = 2x
For 1….1000 = 3*x^2
15. Given 3 lines in the plane such that the points of intersection form a triangle with sides of
length 20, 20 and 30, the number of points equidistant from all the 3 lines is
a)1
b)3
c)4
d)0
Ans: 4
16. Hare in the other. The hare starts after the tortoise has covered 1/3 of its distance and that
too leisurely. A hare and a tortoise have a race along a circle of 100 yards diameter. The
tortoise goes in one direction and the. The hare and tortoise meet when the hare has covered
only 1/8 of the distance. By what factor should the hare increase its speed so as to tie the
race?
a) 30.33
b)8
c) 40
d) 5
Ans: 30.33
Sol: 1/3, 1/8
3*8=24
(24-3)=21
(21-8)=13
(21*13)/3^2
17. Here 10 programmers, type 10 lines with in 10 minutes then 60lines can type within 60
minutes. How many programmers are needed?
a) 16
b) 6
c) 10
d) 60
Solution: (men*time)/work)
Ans: 10
This type of Q's repeated 4times for me but values are different.
18. Alok and Bhanu play the following min-max game. Given the expression N = 9 + X + Y -
Z Where X, Y and Z are variables representing single digits (0 to 9) Alok would like to
maximize N while Bhanu would like to minimize it. Towards this end, Alok chooses a single
digit number and Bhanu substitutes this for a variable of her choice (X, Y or Z). Alok then
chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes
the value for the remaining variable. Assuming both play to their optimal strategies, the value
of N at the end of the game would be.
a) 0
b) 27
c) 18
d) 20
The Q's concept is same but the equation of N's is changing.
19. Alice and Bob play the following coins-on-a-stack game. 20 coins are stacked one above
the other. One of them is a special (gold) coin and the rest are ordinary coins. The goal is to
bring the gold coin to the top by repeatedly moving the topmost coin to another position in
the stack.Alice starts and the players take turns. A turn consists of moving the coin on the top
to a position i below the top coin (0 = i = 20). We will call this an i-move (thus a 0-move
implies doing nothing). The proviso is that an i-move cannot be repeated; for example once a
player makes a 2-move, on subsequent turns neither player can make a 2-move. If the gold
coin happens to be on top when it's a player's turn then the player wins the game. Initially, the
gold coins the third coin from the top. Then
a) In order to win, Alice's first move should be a 1-move.
b) In order to win, Alice's first move should be a 0-move.
c) In order to win, Alice's first move can be a 0-move or a 1-move.
d) Alice has no winning strategy.
Ans: d
20. For the FIFA world cup, Paul the octopus has been predicting the winner of each match
with amazing success. It is rumored that in a match between 2 teams A and B, Paul picks A
with the same probability as A's chances of winning. Let's assume such rumors to be true and
that in a match between Ghana and Bolivia, Ghana the stronger team has a probability of 2/3
of winning the game. What is the probability that Paul will correctly pick the winner of the
Ghana-Bolivia game?
a)1/9
b)4/9
c)5/9
d)2/3
Ans: 5/9
Q21. 36 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In other words,
there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36,
a1}. Then size of the smallest set of people such that the rest have shaken hands with at least
one person in the set is
a)12
b)11
c)13
d)18
Ans: 12
22. After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters
randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1
letter is inserted in an improper envelope?
a)1/12
b)0
c)12/212
d)11/12
Ans: b
23. A sheet of paper has statements numbered from 1 to 40. For each value of n from 1 to 40,
statement n says "At least and of the statements on this sheet are true." Which statements are
true and which are false?
a) The even numbered statements are true and the odd numbered are false.
b) The first 26 statements are false and the rest are true.
c) The first 13 statements are true and the rest are false.
d) The odd numbered statements are true and the even numbered are false.
Ans: c
24. There are two boxes, one containing 10 red balls and the other containing 10 green balls.
You are allowed to move the balls between the boxes so that when you choose a box at
random and a ball at random from the chosen box, the probability of getting a red ball is
maximized. This maximum probability is
a)1/2
b)14/19
c)37/38
d)3/4
Ans: 14/19
25. A circular dartboard of radius 1 foot is at a distance of 20 feet from you. You throw a dart
at it and it hits the dartboard at some point Q in the circle. What is the probability that Q is
closer to the center of the circle than the periphery?
a) 0.75
b) 1
c) 0.5
d) 0.25
Ans: d
26. On planet zorba, a solar blast has melted the ice caps on its equator. 8 years after the ice
melts, tiny plantoids called echina start growing on the rocks. echina grows in the form of a
circle and the relationship between the diameter of this circle and the age of echina is given
by the formula d = 4 * sqrt (t – 8)for t = 8 Where the represents the diameter in mm and t the
number of years since the solar blast. Jagan recorded the time of some echina at a particular
spot is 24 years then what is diameter?
a) 8
b) 16
c) 25
d) 21
Ans: 16
27. A sheet of paper has statements numbered from 1 to 40. For all values of n from 1 to 40,
statement n says: 'Exactly n of the statements on this sheet are false.' Which statements are
true and which are false?
a) The even numbered statements are true and the odd numbered statements are false.
b) The odd numbered statements are true and the even numbered statements are false.
c) All the statements are false.
d) The 39th statement is true and the rest are false.
Ans: d
28. Alok and Bhanu play the following coins in a circle game. 99 coins are arranged in a
circle with each coin touching two other coin. Two of the coins are special and the rest are
ordinary. Alok starts and the players take turns removing an ordinary coin of their choice
from the circle and bringing the other coins closer until they again form a (smaller) circle.
The goal is to bring the special coins adjacent to each other and the first player to do so wins
the game. Initially the special coins are separated by two ordinary coins O1 and O2. Which of
the following is true?
a) In order to win, Alok should remove O1 on his first turn.
b) In order to win, Alok should remove one of the coins different from O1 and O2 on his first
turn.
c) In order to win, Alok should remove O2 on his first turn.
d) Alok has no winning strategy.
Ans: a if the gold coin in 3rd position then mark it otherwise leave it
29. Two pipes A and B fill at A certain rate B is filled at 10, 20, 40, 80. If 1/4 of B if filled in
21 hours what time it will take to get completely filled
Ans: 23
30. One day Alice meets pal and byte in fairyland. She knows that pal lies on Mondays,
Tuesdays and Wednesdays and tells the truth on the other days of the week byte, on the other
hand, lies on Thursdays, Fridays and Saturdays, but tells the truth on the other days of the
week. Now they make the following statements to Alice – pal. Yesterday was one of those
days when I lie byte. Yesterday was one of those days when I lie too. What day is it?
a) Thursday b) Tuesday c) Monday d) Sunday
Ans: a
.
31. Sudha Patel +> perfume factory
Ans : 2 more cedar
32. A toy train can make 10 sounds sound changes after every 4 minute now train is defective
and can make only 2 sounds find probability that same sound is repeated 4 times
consecutively (1 OUT OF__)?
a 16
b 8
c 12
d 4
Ans:
(1/2)*(1/2)*(1/2)*(1/2)+ (1/2)*(1/2)*(1/2)*(1/2)=(1/8)
thus 1 out of 8 ans
33. In there is a planet Oz in which there is 36 hrs in a day & 90 minutes in a hrs and 60
seconds in 1 minute it is having same pattern as our watch. Then what will be angle between
hour hand and minute hand at 9:40?
a) 29
b) 12
c) 67
d) 98
Ans :29
34. In a country x we are having diff types of coins ranging from 64…512. All coins having
different integral value the difference between two coins comes out to be 50% more than the
former coin. Then how many coins can be made?
Ans : 6 coins
Sol.64
64*1.5=96
96*1.5=144
144*1.5=216
216*1.5=324
324*1.5=486
Then total coin will be 6
35. There is a relation is given which is n/P=195 Where n- no of steps in meters P- pace
length These Is a man shivam he know his pace length =185cm then what will be the speed
of shivam kmph?
Ans=195*1.85*1.85*60/1000=40.04kmph
Aptitude Questions
1.A bookseller sells a particular novel at 10% discount on the labelled price. Also he is so
generous that he gives a free book for every 15 books for wholesale buyers. In this
transaction his gain is 35%. Then find the ratio of Ratio of Labelled Price to the actual CP.
Answer :
Lets assume the CP of each book be 100. Hence CP of 16 books would be 1600.
SP of 15 books = 1600 + (1600 * 35/100) = 2160.
SP of each book would be 2160/15 = 144.
If SP of each book is 90, labelled price would be 100 (since he gives at a 10% discount).
Hence if SP is 144 marked price would be 144*(100/90) = 160.
Ratio of Labelled Price to the actual CP = 160/100 = 8/5.
2.If a pen is being sold at 4% profit instead of 4% loss the actual profit is Rs 16. What is the
actual cost price of the pen?
Answer :
Let x be the CP.
(104/100)x - (96/100)x = 16
Solving we get x = Rs.200.
3.A cake seller sells one cake at a profit of 10% and sells another at a loss of 5%. Let the
ratio of the CPs of the cakes is 2:3 respectively. Find his net profit or loss percentage.
Answer :
Let the CPs of the cakes be 2x and 3x (so that they are in the ration 2:3 as per the
question.)
Hence net CP = 5x.
SP of first cake = (110/100)*2x = 220x/100
SP of second cake = (95/100)*3x = 285x/100
Net SP = (220x/100) + (285x/100) = 505x/100 = 5.05x.
SP is greater than CP and his profit is 5.05x - 5x = .05x.
His profit percentage = (.05x/5x)% = .01%.
4) A man can row 5 kmph in still water. If the river is running at 1kmph, it takes him 75
minutes to row to a place and back. How far is the place?
(i) 3km
(ii) 2.5 km
(iii) 4 km
(iv) 5 km
Answer: 3 Km
Solution:
Speed downstream = (5+1)km/hr = 6 km/hr Speed upstream = (5-1)km/hr = 4 km/hr Let the
required distance be x km x/6 + x/4 = 75/60 2x+3x = 15 x = 3km
5) 729 ml of a mixture contains milk and water in ratio 7:2. How much of the water is to be
added to get a new mixture containing half milk and half water?
(i) 79 ml
(ii) 81 ml
(iii) 72 ml
(iv) 91 ml
Answer: 81 ml
Solution:
Milk = (729 * (7/9))=567ml
Water = (729-567)= 162ml
Let water to be added be x ml 567/(162+x) = 7/3 1701 = 1134 + 7x x = 81ml
6) If log 0.317=0.3332 and log 0.318=0.3364 then find log 0.319?
(i)0.3396
(ii)0.3369
(iii)0.3368
(iv)0.3338
Answer: 0.3396
Solution:
log 0.317=0.3332 and log 0.318=0.3364, then log
0.319=log0.318+(log(0.318-0.317)) = 0.3396
7) A box of 150 packets consists of 1kg packets and 2kg packets. Total weight of box is
264kg. How many 2kg packets are there?
(i)36
(ii)114
(iii)120
(iv)50
Answer: 114
Solution:
x= 2 kg Packs
y= 1 kg packs
x + y = 150 ----------------(1)
2x + y = 264 ---------------(2)
Solve the Simultaneous equation; x = 114,y=36
ANS : Number of 2 kg Packs = 114.
8) In a hotel, rooms are numbered from 101 to 550. A room is chosen at random. What is
the probability that room number starts with 1, 2 or 3 and ends with 4, 5 or 6?
Answer
There are total 450 rooms.
Out of which 299 room number starts with either 1, 2 or 3. (as room number 100
is not there) Now out of those 299 rooms only 90 room numbers end with 4, 5 or
6.So the probability is 90/450 i.e. 1/5 or 0.20.
9) What is the four-digit number in which the first digit is 1/3 of the second, the third is the
sum of the first and second, and the last is three times the second?
Answer
The 4 digit number is 1349.
10) Difference between Bholu's and Molu's age is 2 years and the difference between
Molu's and Kolu's age is 5 years. What is the maximum possible value of the sum of the
difference in their ages, taken two at a time?
Answer
The maximum possible value of the sum of the difference in their ages -
taken two at a time - is 14 years.
11) A 3 digit number is such that it's unit digit is equal to the product of the other two
digits which are prime. Also, the difference between it's reverse and itself is
396.What is the sum of the three digits?
Answer
The required number is 236 and the sum is 11.
12) Pepsi, Fanta, Cola order either coffee or tea after dinner. a)If pepsi orders coffee, Fanta
orders the drink that is ordered by cola. b)If fanta orders coffee, pepsi do not order the
drink that is ordered by cola. c)If cola orders tea, pepsi orders the same drink ordered by fanta. Who take the same drink every day?
Ans:Pepsi.
13) Boat A leaves shore P and Boat B leaves shore Q.(P and Q are opposite shores of a
river.) A and B travel at constant speed. But the speeds are not same. Both boats meet at
600m from P for the first time. In their return journeys (i.e. after touching the shores), they
meet again at 200m from Q. Find distance between P and Q.
Ans: 1600m
14) There are two glasses A and B. A contains orange juice and B contains apple juice in
same quantity. Some amount orange juice from glass A is transferred to glass B. The juice
in glass B is mixed well. Then again the same amount of juice from B is transferred to A.
Compare the quantities of apple juice in A and orange juice in B.
Ans: Equal.
15) 100 Kg. Potatoes with 98% water content are dried in an oven. The percentage of water
decreases to 50 %. What is the weight of potatoes now?
Ans: 4Kg.
16) A 31" x 31" square metal plate needs to be fixed by a carpenter on to a wooden board.
The carpenter uses nails all along the edges of the square such that there are 32 nails on
each side of the square. Each nail is at the same distance from the neighbouring nails.
How many nails does the carpenter use?
Solution: 32*2 + 30*2=124
Latest Aptitude Questions with solutions
1) Eight friends Harsha, Fakis, Balaji, Eswar, Dhinesh, Chandra, Geetha, and Ahmed are
sitting in a circle facing the center.
Balaji is sitting between Geetha and Dhinesh. Harsha is third to the left of Balaji and
second to the right of Ahmed. Chandra is sitting between Ahmed and Geetha and Balaji
and Eshwar are not sitting opposite to each other. Who is third to the left of Dhinesh?
Answer: Fakis
Explanation: Arranging the friends as per the question statement we can arrive at the following
diagram
Ahmed
Fakis Chandra
Harsha Geetha
Eswar Balaji
Dhinesh
Hence correct answer is Fakis
2) A fast typist can type some matter in 2 hours and a slow typist can type the same in 3
hours. If both type jointly, in how much time will they finish?
Answer: 1 hr 12 min
Explanation : The fast typist's work done in 1 hr = 1/2
The slow typist's work done in 1 hr = 1/3
If they work jointly, work done in 1 hr = 1/2+1/3 = 5/6
So, the work will be completed in 6/5 hours. i.e., 1+1/5 hours = 1hr 12 min
3) Today is 4.11.09. Keeping that figure 41109 in mind, i have arrived at the following
sequence: 2, 1, 9, 5, _ Which of the following four numbers can fill the dash?
Options
a) 7
b) 65
c) 4563
d) 262145
Answer : 41109
1^4 + 1 = 2
1^1 + 0 = 1
0^1 + 9 = 9
9^0 + 4 = 5
So next is 4^9 + 1 = 262145
4) Let S be a Set of some positive integral numbers; with an average of 47; and containing
the number 83. The numbers may or may not be distinct .However ; when the number 83 is
removed ; the Avg drops to 46 .What is the largest number that can be possibly contained
in that Set ?
Solution:
Let S be the sum of that set of n positive integers. S/n = 47
(S - 83)/(n - 1) = 46
Solving the above 2 equations, we get S = 1739; n = 37.
This set of 37 positive integers contains 83. To get to the expected answer, we have to
Suppose that 35 of the remaining 36 integers has a value of 1 each (least +ve integer).
Thus, the largest possible integer in the set = 1739 - 83 - 35*1 = 1621
5) Sum of squares of two numbers 'x' and 'y' is less than or equal to 100. How many sets
of integer solutions of 'x', 'y' is possible?
Answer: Total 317 solutions
Explanation:
x = 0, |y| <= 10 -> 21 solutions
|x| = 1, |y| <= 9 -> 38 solutions
|x| = 2, |y| <= 9 -> 38 solutions
|x| = 3, |y| <= 9 -> 38 solutions
|x| = 4, |y| <= 9 -> 38 solutions
|x| = 5, |y| <= 8 -> 34 solutions
|x| = 6, |y| <= 8 -> 34 solutions
|x| = 7, |y| <= 7 -> 30 solutions
|x| = 8, |y| <= 6 -> 26 solutions
|x| = 9, |y| <= 4 -> 18 solutions
|x| = 10, y = 0 -> 2 solutions
6) There is a unique number of which the square and the cube together use all ciphers
from 0 up to 9 exactly once. Which number is this?
Answer: The number is 69.
Explanation:
69^2=4761 and 69^3=328509..
7) You are standing next to a well, and you have two jugs. One jug has a content of 3
litres and the other one has a content of 5 litres. How can you get just 4 litres of water
using only these two jugs?
Solution:
Fill 3 litre jug pour to 5 litre jug
Fill again 3 litre jug and add to 5 litre jug then 1 litre will be there in 3 litre jug
Pour all water outside from 5 litre jug
Fill 1 litre water from 3 litre jug to 5 litre jug
Fill 3 litre jug and add to 5 litre jug making it 4 litres of water.
8) Blocks are chosen randomly on a chessboard. What is the probability that they are in
the same diagonal?
Answer:
There are total of 64 blocks on a chessboard. So 3 blocks can be chosen out
of 64 in 64C3 ways.
So the sample space is = 41664
There are 2 diagonal on chessboard each one having 8 blocks. Consider one of them.
3 blocks out of 8 blocks in diagonal can be chosen in 8C3 ways.
But there are 2 such diagonals, hence favourables = 2 * 8C3 = 2 * 56 = 112
The required probability is
= 112 / 41664
= 1 / 372
= 0.002688
9) What is the area of the triangle ABC with A(e,p) B(2e,3p) and C(3e,5p)?
where p = PI (3.141592654)
Answer:
A tricky ONE.
Given 3 points are collinear. Hence, it is a straight line.
Hence area of triangle is 0.
10) Silu and Meenu were walking on the road.Silu said, "I weigh 51 Kgs. How much do you
weigh?" Meenu replied that she wouldn't reveal her weight directly as she is overweight.
But she said, "I weigh 29 Kgs plus half of my weight”. How much does Meenu weigh?
Answer
Meenu weighs 58 Kgs.
It is given that Meenu weighs 29 Kgs plus half of her own weight. It means that
29 Kgs is the other half. So she weighs 58 Kgs.
Solving mathematically, let's assume that her weight is X Kgs.
X = 29 + X/2
2*X = 58 + X
X = 58 Kgs
11)Consider the sum: ABC + DEF + GHI = JJJ .If different letters represent different digits,
and there are no leading zeros, what does J represent?
Answer
The value of J must be 9.Since there are no leading zeros, J must be 7, 8, or 9. (JJJ = ABC
+ DEF + GHI= 14? + 25? + 36? = 7??)Now, the remainder left after dividing any number by 9
is the same as the remainder left after dividing the sum of the digits of that number by 9.
Also, note that 0 + 1 + ... + 9 has a remainder of 0 after dividing by 9 and JJJ has a
remainder of 0, 3, or 6. The number 9 is the only number from 7, 8 and 9 that leaves a
remainder of 0, 3, or 6 if you remove it from the sum 0 + 1 + ... + 9. Hence, it follows that J
must be 9.
12) Using two 2's and two 3's and using a maxim of three mathematical signs, symbols,
can you have a result in between 14 and 15? Concatenation (clubbing of digits) allowed.
Solution:
( 23 + 3! ) / 2 = 14.5
18) What is the 28383rd term in the series 1234567891011121314............
a) 3
b) 4
c) 7
d) 9
Solution:
there are 9 no. of single digit
there are 180 no. of double digit
there are 2700 no. of three digit
now total 2889 no. till 999
remaining no. are 25494 that is divided by 4 and the q is 6373 with reminder of 2 so 28381
is 6373+999=737(2)
n next no is 7(3)73
so ans is 3
13) a*b*c*d*e + b*c*d*e*f + a*c*d*e*f + a*b*d*e*f + a*b*c*e*f + a*b*c*d*f = a*b*c*d*e*f and
a,b,c,d,e and f are all positive nonrepeating integers then solve a,b,c,d,e, and f.
Solution :
Start with 1/2 + 1/2, then progressively split the last part x
into 2x/3 + x/3. This gives the following progression:
2,2
2,3,6
2,3,9,18
2,3,9,27,54
2,3,9,27,81,162
14) 729 ml of a mixture contains milk and water in ratio 7:2. How much of the water is to be
added to get a new mixture containing half milk and half water?
(i) 79 ml
(ii) 81 ml
(iii) 72 ml
(iv) 91 ml
Solution:
Milk = (729 * (7/9))=567ml
Water = (729-567)= 162ml
Let water to be added be x ml l 567/(162+x) = 7/3 1701 = 1134 + 7x x = 81ml
15) If one-seventh of a number exceeds its eleventh part by 100 then the number is…
(i) 770
(ii) 1100
(iii) 1825
(iv) 1925 Solution:
Let the number be x. Then X/7 - x/11 =100 11x-7x = 7700 x=1925.
16) If 1.5x=0.04y then the value of (y-x)/(y+x) is
(i) 730/77
(ii) 73/77
(iii) 7.3/77
(iv) None
Solution:
x/y = 0.04/1.5 = 2/75
So (y-x)/(y+x) = (1 - x/y)/(1 + x/y) = (1 - 2/75)/ (1 + 2/75) = 73/77.
17) The smallest number which when diminished by 3 is divisible by 21, 28, 36 and 45 is...
(i) 869
(ii) 859
(iii) 4320
(iv) 1263
Solution:
The required number = l.c.m. of (21, 28, 36 ,45)+3=1263
18) If x and y are the two digits f the number 653xy such that this number is divisible by 80,
then x+y is equal to:
(i) 2
(ii) 3
(iii) 4
(iv) 6
Solution:
Since 653xy is divisible by 2 as well as by 5, so y = 0
Now 653x0 is divisible by 8 so 3x0 is also divisible by 8.
By hit and trial x=6 and x+y = 6
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