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# G.P.R.E.C ,Kurnool. ,13 September 2011 by TCS

Details of G.P.R.E.C ,Kurnool. ,13 September 2011 by TCS conducted by TCS for job interview.
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WRITTEN TEST:
1. (1/2) Of A Number Is 3 Times More Than The (1/6) Of The Same Number?
Solution:1/2x=3+1/6x =>x=9

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 1/32 filled of the 21 hours, what is total duration of hours required to fill it completely?
a) 26 B)25 c)5 d)27

Solution: for every hour water in tank in B is doubled,
Let the duration to fill the tank B is x hours.
X/32 part of water in tank of B is filled in 21 hours,
Next hour it is doubled so,
2*(x/32) part i.e (x/16) part is filled in 22 hours,
Similarly (x/8) th part in 23 hours,(x/4)th part is filled in 24 hours,
(x/2) th part is filled in 25 hours, (x) th part is filled in 26 hours

3. 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
(2 Questions are given of this model.)

4. 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

Solution: 490/(4*35)

5. 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?
0.75
1
0.5
0.25
solution:0.25
If it is a circular dartboard : (PI*((r/2)^2))/(PI*(r^2))=0.25
If it is a square dartboard : (PI*((r/4)^2))/(r^2)=(app)0.2

6. 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?

4/9
2/3
1/9
5/9

Solution:(1/3*1/3)+(2/3*2/3)=5/9

7. 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
buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?

256
54
192
64

Solution:From 1 to 1000 number of 3,s are 300.
Since they mentioned 8 fingered we have to take base 8.
i.e., (3*(8^2))+(0*(8^1))+(0*(8^0))=192

8. 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

12
13
18
11

Solution: for at least one person & for exactly one person =36/3
for at least two person & for exactly two person =36/2

9. 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

4
3
0
1

Solution: For 3 lines of intersection the answer is 4
For 3 linesegments of intersection the answer is 1

10. 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
27
18
20

Solution: 9+11=20
For X+Y-Z=11,X*(Y-Z)=18, X-Y-Z=2

11. 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?

0
12/212
11/12
1/12

12. 10 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 suspects are lying or the leftmost suspect is innocent.
B. All suspects are lying and the leftmost suspect is innocent .

A only
Neither A nor B
Both A and B
B only

All suspects are lying or the leftmost suspect is innocent.
All suspects are lying and the leftmost suspect is innocent .
Both can satisfy the situation so answer is "Both A and B"
(we have to take only truth values)

13. In the reading room of a library, there are 23 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
Solution: 23 reading spots, Each reading spot consists of 9 chairs placed around it so There are some readers such that in each occupied reading spot there are different numbers of readers. For each table different no of persons are sat,so for first table 1 person is sit,2nd table 2 persons are sit 36

14. 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
Solution: Number of matches=2^8
Number of teams=2^8-1
Number of members left in 1st round=128

15. There is 7 friends (A1, A2, A3....A7).If A1 have to have shake with all without repeat. How many handshakes possible?
a) 6
b) 21
c) 28
d) 7
Solution:6

16. 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
Solution: ((1/2)*1)+((1/2)*(9/19))=14/19

17. 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 9:40 am.
a. 251
b.111
c.29
d.89
Ans.: c
For 12:40 am Ans.. z 89
Formule: 20H-(34/9)M

18. The pacelength P is the distance between the rear of 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.
23.62
11.39
8.78
236.16
Ans.:a
(144*164*164*60)/(10^7)

19. How many 4 digit numbers can be formed using the digits 1, 2,3,4 ,5 ( but with repetition) that are divisible by 4?
Ans.. 5^3

20. There are 6 beer bottle nd one is poisoned. we have mice who will die within 14 hrs after drinkin poisned beer. In 24 hrs we have to find poisoned beer bottle. How many no of mice we require to find out poisoned bottle.
options
a) 6
b) 4
c) 3
d) 1
6 is near to 2^3

21. keyword: Alok Bhanu, stack of 20 coins. i move can play. dat z 1th move meAns. to put top coin 1 postion below. gold coin. initialy gold coin is at 3rd position from top. if itz player turns nd player brings gold coin to the top then player z winner. alok starts. which of the following is true.
a) alok must play 1th move to win.
b) alok must play 0th move to win
c) alok has no wining strategy
Ans. a

22. A hollow cube of size 5 cm is taken, with a thickness of 1 cm. 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?
800
500
488
900
Ans.:side of cube = 5 cm
its thichness = 1 cm
so volume of outer cube = 5*5*5
volume of inner cube = 3*3*3
volume of the hollow cube = 5*5*5 3*3*3 = 98
so total no of small cubes of the size 1 cm = 98/1*1*1 = 98
we know a cube has 6 faces so total no of face = 98*6 = 588
one surface of outer cube contains a total of 25 surface of smaller cube , so when 4 surface of outer cube is painted total no of surface of small cubes i.e supposed to be painted is 4*25 = 100
so the total no of surfaces of small cube that will be remained unpainted is 588-100 = 488
no of faces remain unpainted: 588-( 25* no faces painted)

23. 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.

24. 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?
Ans. 12 min
prgrmr*min/ loc= prgmr *min/ loc
This question was also repeated thrice.
a) no of Programmer
b) no lines of codes
c) how much time they will take.

25.There are 6 circles on a diagonal of square such that their centre lie on diagonal. Consider that radius of each circle is equal. Find the ratio between side of square and radius of circle.
10r+ 2sqrt(2)r= sqrt(2)a
find a/r.

26. On a sheet of paper, there are 40 statements. Each n statement states that "Atleast n number of statements on this sheet is false". Then which of the following is true.

Answer: first 20 statements are true and last 20 are false.
This question was also repeated thrice.
a) Atleast wid false Ans. first 20 r true and last 20 r false..
b) Exactly wid true Ans. 39th z true nd rest r false
c) Atmost wid true or false Ans. all statements r true

27. 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* (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