Thursday 16 August 2012

TCS extra Aptitude Questions - Recruitment On 2011

 TCS Xtra Aptitude Questions - 1/3 Recruitment 2011

1. 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) 12 (b) 13 (c) 10 (d) 15
Soln:
Let ages be x,y,z then,
y-x=3 → y=x+3
z=3x
z=x+y+2
→ 3x = x+x+3+2
x=5
z=15
Ans: d
2. 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 7 pennies and got the same amount of each type of fruit for each of his three children. What did each child get?
(a) 1 apple, 2 chickoos, 2 peanuts
(b) 1 apple, 2 chickoos, 1 peanut
(c) 1 apple, 3 chickoos, 2 peanuts
(d) 1 apple, 1 chickoos, 1 peanut

Soln:
Spent 7p.
Each child gets 1 apple --> Father spent 3p on 3 apples.
Remaining 4p.
Suppose each child gets 2 chickoos --> Father spent 3p on 6 chickoos
Remaining 1p
Now if each child gets 1 peanut --> Father spent 1p on 3 peanuts.
Hence each child gets 1 apple, 2 chickoos, 1 peanut.
Ans: b

3. 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 and 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) 12 (b) 18 (c) 6 (d) 72

Soln:
programmers1 * time1 /lines1 = programmers2 * time2 / lines2
12*12/12 = 72 * x/72
--> x=12
Ans: a
4. 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) 20 (b) 18 (c) 27 (d) 0

Soln:
We have tricks for this type of problems as,
x+y-z=11, x-y-z=2 and x*(y+z)=18
Here solution=11+9 =20
Ans: a
5. 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) Monday (b) Sunday (c) Thursday (d) Saturday

Soln:
please see TCS Sample Aptitude Questions 3 - Recruitment 2011
Ans: c

6. 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) 192 (b) 64 (c) 54 (d) 102

Soln:
3, 13, ..., 73 --> 8
113,...
.
.
.
713, ..., 773 -->
No of 3s in 1s place = 8*8 = 64

Similarly No of 3s in 10s place = 8*8 = 64
No of 3s in 100s place = 8*8 = 64
Total no of 3s = 3*64 = 192
Ans: a
7. On planet zorba, a solar blast has melted the ice caps on its equator. 8 years after the ice melts, tiny planetoids 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 * √ (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) 8 (b) 12 (c) 16 (d) 24
Soln:
Please see TCS Sample Aptitude Questions 4 - Recruitment 2011
Ans: d
8. 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 centre of the circle than the periphery?
                  (a) 1/4 (b) 1/2 (c)3/4 (d) 1/3
Soln:
Please see TCS Sample Aptitude Questions 4 - Recruitment 2011
Ans: a
9) A schoolyard contains only bicycles and 4 wheeled wagons. On Tuesday, the total number of wheels in the schoolyard was 166. What could the possible number of bicycles?
                           (a) 14 (b) 10 (c) 12 (d) 11

Soln:
Let x bicycles & y 4 wheeled wagons. then
2x+4y = 166
Put x=11 --> 4y= 166 - 22 = 144, y=36
Ans: d
10) 9years ago, Andromeda’s age was twice Achilles’ age .9 years hence, Andromeda’s age will be 4/3 times the age of Achilles’. Find Andromeda’s present age in binary numbers.
               (a)11011 (b) 11000 (c) 1001 (d) 1010
Soln:
present Andromeda's age --> x and Achille's age --> y
               x-9 = 2(y-9)
             x+9 = 4/3(y+9)
Solving
              -18 = 2/3 y + (-18-12)
               2y = 12 * 3
we get x = 27 and y = 18
27 in binary = 11011       
Ans: a
11. After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?
               (a) 11/12 (b) 0 (c) 1/12 (d) 1/6

Soln:
Please see TCS Sample Aptitude Questions 4 - Recruitment 2011
Ans: b
12. 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) 375 (b) 625 (c) 500 (d) 3125
Soln:
Please see TCS Sample Aptitude Questions 4 - Recruitment 2011 .
Ans: b
13. 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) 0 (c) 4 (d) 2
Soln:
Please see TCS Sample Aptitude Questions 4 - Recruitment 2011.
Ans: c
14) 21 people meet and shake hands. The maximum number of handshakes possible if there is to be no ‘cycle’ of handshakes is (A cycle of handshakes is a sequence of people a1, a2, … ,aK
such that the pairs (a1, a2), (a2, a3), … , (a (k-1), a k) , (ak, a1) shake hands.
                (a) 17 (b) 18 (c) 19 (d) 20
Soln:
             Since no cycle, answer = n-1 = 20
Ans: d
15) The ticket to Disneyland will cost anywhere from 1p to 63p. You need to produce the exact change as the ticket counter and have with you a 63p coin. So you decide to break this into change but you want to carry with you as few coins as possible. Assuming that coins of all denominations are available, how many coins (denominations) would you split the 63p into?
                     (a) 33 (b) 63 (c) 6 (d) 64
Soln: 63 can be split into 1,2,4,8,16,32.
--> no of coins = 6
Ans: c
16. For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumoured 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 rumours 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) 5/9 (b) 1/9 (c) 2/3 (d) 1/3
Soln:
Please see TCS Sample Aptitude Questions 5 - Recruitment 2011
Ans: a
17. 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) 18 (b) 13 (c) 34 (d) None
Soln:
The smallest set can be formed selecting ak and eliminating ak-1 & ak+1.
--> Size of smallest set = 36/3
                                = 12
Ans: d
18. One 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, hour hand covers the dial twice every day. Find the approximate angle between the hands of clock on Oz when time is 12.40 am
                       (a) 89 (b) 251 (c) 111 (d) 79
Soln:
Please see TCS Sample Aptitude Questions 5 - Recruitment 2011
Ans: a

19. The IT giant Tirnop has recently crossed a head count of 150000 and earning 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?
                       (a) 6 (b) 432 (c) 72 (d) 12
Soln:
            12p 12m 12l
            1 12 1
            1 72 6
            72 72 6*72
Ans: b
20. 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 pained totally how many faces of the smaller cubes remain unpainted?
                  (a) 900 (b) 488 (c) 500 (d) 800
Soln:
Please see TCS Sample Aptitude Questions 5 - Recruitment 2011
Ans: b
21. Planet fourfi resides in 4 – dimensional space and thus the currency used by its residents are 3 – dimensional objects. The rupees 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.

    The diameter of the coins should be at least 64mm and not exceed 512mm
    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.

You are asked to design a set of coins of different diameters with these requirements and your goal is to design as many coins as possible. How many coins can you design?
             (a) 5 (b) 8 (c) 9 (d) 6
Soln:
Please see TCS Sample Aptitude Questions 5 - Recruitment 2011
Ans: d
22. A hare and tortoise 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 tortoise has covered 1/5 its distance and that 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) 40 (d) 5
Soln:
Please see TCS Sample Aptitude Questions 5 - Recruitment 2011
Ans: b
23. 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) 1:(2 + 7 √2) (b) 1:(4 + 7 √3) (c) (2 + 7√ 2):1 (d) 1:(2 + 6√ 2)

Soln:
Please see TCS Sample Aptitude Questions 5 - Recruitment 2011
Ans: d
24. 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 streetlegal vehicles in1947 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) 15.88 (b) 29.75 (c) 14.88 (d)476
Soln:
         time = 952/34
= 14.88
Ans: c
25. 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 is maximized. This maximum probability is
              a)37/38 (b) 1 / 2 (c) 14/19 (d) 3 / 4
Soln:
Please see TCS Sample Aptitude Questions 5 - Recruitment 2011
Ans: c

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