TCS latest questions with solutions - 2015 -Part 2

1. problemsolvingproblemsolvingprob . . . . . . Find the 2015th term in the series? 
Sol.
Problemsolving = 14 letter word. So divide 2015 by 14 and find the remainder. Here remainder is 13. so 13th letter in problemsolving is 'n'

2. 4 men can check exam papers in 8 days working 5 hours regularly. What is the total hours when 2 men will check the double of the papers in 20 days?
Sol. 
Let a man can do 1 unit of work in 1 hour.  
Total units of work = 4 x 8 x 5 = 160 units.
Now work = 2 x 160 = 320 units. 
Now 2 men work for 20 days. Let in x hours they have to work per day.
Now total work = 2×x×20 = 40 x 
40x = 320  So x = 320/40 = 8 hours.  

3. X = 101102103104105106107......146147148149150  (From numbers 101-150).  Find out the remainder when this number is divided by 9.

Sol:

The divisibility rule for 9 is sum of the digits is to be divisible by 9.  So 

We calculate separately, sum of the digits in hundreds place, tenths place, and units place. 

Sum of the digits in hundreds place: 1 x 50 = 50

Sum of the digits in tenths place : 0 x 9 + 1 x 10 + 2 x 10 + 3 x 10 + 4 x 10 + 5 x 1 = 105

Sum of the digits in units place : (1 + 2 + 3 + ...+ 9) x 5 = 225

So total = 380

So remainder = 380 / 9 = 2

4. A number is 101102103104...150. As 101 102 103 103.... 150. What is reminder when divided by 3?  
Sol. Divisibility rule for 3 also same as 9. so from the above discussion sum of the digits = 380 and remainder = 380/3 = 2.

5. In 4 years, Raj's father age twice as raj, Two years ago, Raj's mother's age twice as raj. If Raj is 32yrs old in eight yrs from now, what is the age of Raj's mother and father?  
Sol. Raj present age = 32 - 8 = 24.
After 4 years Raj's age is 28. and Raj's fathers age is 28 x 2 = 56, and his present age is 52.
Two years ago, Raj's age is 22. and his mother's age is 22 x 2 = 44. His mother's present age = 46

6. 7^1+7^2+7^3+.......+7^205. Find out how many numbers present which unit place contain 3?
Sol. Units digits of first 4 terms are 7, 9, 3, 1. and this pattern repeats. So for every 4 terms we get one term with 3 in its unit digit. So there are total of 205/4 = 51 sets and each set contains one terms with 3 in its unit digit. 
Ans is 51. 

7. In paper A, one student got 18 out of 70 and in paper B he got 14 out of 30. In which paper he did fare well?
Sol. Find the percentages. Paper A = 18/70 x 100 = 25.7
Paper B = 14/30 x 100 = 46.6

8. Find the total no of divisors of 1728 (including 1 and 1728)
Sol. Direct formula from our lesson on factors. Click Here. 
The number of factors or divisors of a number N=ap.bq.cr... = (p+1).(q+1).(r+1)... where a, b, c ... prime numbers. 
1728 = 26×33
So total number of divisors = (6 + 1).(3 + 1) = 28

9. The sum of two numbers is 45. Sum of their quotient and reciprocal is 2.05, Find the product of the numbers.
Sol: Let a, b be the numbers. 
a + b = 45
ab+ba = 2.05
⇒a2+b2ab = 2.05
⇒(a+b)2−2abab=2.05
⇒(a+b)2 = 2.05ab + 2ab = 4.05ab
⇒ ab = 4524.05 = 500

10. A number is divided by 406 leaves remainder 115 , What will be the reminder when it will be divided by 29?
Sol. Let the number be N.
So N = 406x + 115. 
Now divide this number by 29. As 406 is exactly divisible by 29, we have to divide 115 by 29 and find the remainder. So remainder = 28

11. (p/q-q/p)=21/10. Then find 4p/q+4q/p?
sol. 
Let p/q = a, then (a - 1/a) = 21/10
⇒a2−1=a.2110
⇒10a2−21a−10 = 0
Roots of the equation = −b±b2−4ac−−−−−−−√2a
a = 21±441+400−−−−−−−−√20
a = 21±2920 = 5/2 or -2/5
For a = 5/2, 4p/q+4q/p = 58/5
For a = -2/5, 4p/q+4q/p = -58/5

12. Two vertical ladders length of 6 m and 11 m are kept vertically at a distance of 12 m. Find the top distance of both ladders?
Sol:

So distance between the top points = AD = 122+52−−−−−−−√=13

So in paper B he did well.  

Updated:

 13. 

Here is 15 dots.  If you select 3 dots randomly, what is the probability that 3 dots make a triangle?
a. 440/455
b. 434/455
c. 449/455
d. 438/455

Sol.

I think there seem some problem with this question. Total ways of selecting 3 dots out of 15 is 15C3 = 455 If 3 dots are collinear then triangle may not be formed. Now look at the above diagram.  If we select any 3 dots from the red lines they may not form a triangle. They are 3 x 5C3 = 30.  If we select the three letters from blue lines, they may not form a triangle. They are in total 5 ways. Also there are 6 others lines which don't form a triangle.  Also another two orange lines. Total = 30 + 5 + 6 + 2 = 43.  So we can form a triangle in 455 - 43 = 412. So answer could be 412/455.  

14.   In a series of numbers , the next number is formed by adding 1 to the sum of the previous numbers, and the 10th number is 1280.  Then what is the first number in the series? (series will be like this x , x+1, (x+(x+1))+1,....... )
a. 1
b. 4
c. 5
d. None of these
Answer: Option B
Sol. 
The given series is x, x + 1, 2x + 2, 4x + 4 ......
If you observe the pattern here,  the coefficient of x + 1 is in the powers of 2. So 4th term has a power of 2, 5th term has a power of 3... 10th term has a power of 8. So tenth term would be 28(x + 1)
= 256(x+1). 
Given 256(x+1) = 1280 
x = 4. 

15. The number of multiples of 10 which are less than 1000, which can be written as a sum of four consecutive integers is
a. 50
b.100
c. 150
d. 216
Answer: Option A
Sol: 
We can write 10 = 1 + 2 + 3 + 4.  So we have to find how many multiples of 10 can be written in this manner. 
Let the first of the four numbers be n. So 
n + (n+1) + (n+2) + (n+3) = 10k
4n + 6 = 10k
2n + 3 = 5k
n = 5k−32 = 2k – 1 + k–12
So n is intezer for k = an odd number. So for k = 1, 3, 5, .... 99 we can write a number as a sum of four consecutive intezers.
So there are 50 numbers. 

16. Mr. Bean chooses a number and he keeps on doubling the number followed by subtracting one from it, if he chooses 3 as initial number and he repeats the operation for 30 times then what is the final result?
a. (2^30) – 1
b. (2^30) – 2
c. (2^31) – 1
d. (2^31) – 2
Ans: No option
Sol: 
Step 1: (3 x 2) - 1 = 5 ( 2^2 + 1)
Step 2: (5 x 2) - 1 = 9 (2^3 + 1)
Step 3: (9 x 2) - 1 = 17 (2^4 + 1)
Step 4: (17 x 2) - 1 = 33 (2^5 + 1)
So After 30 steps we have 2^31 + 1

17. Tony alone can paint a wall in 7 days and his friend Roy alone can paint the same wall in 9 days. In how many days they can paint the wall working together? Round off the answer to the nearest integer.
a. 3
b. 4
c. 5
d. 7
Answer: Option B
Sol. use formula (xy / x+y) 
So nearest value for 3.93 = 4

18. In this question, A^B means A raised to the power B. Let f(X)=1+X+x^2+....x^6.  The remainder when f(X^7) is divided by f(X) is
a. 0
b. 6
c. 7
d. None of the other 3 choices.
Answer: C
Explanation:
Given that f(x7)=1+x7+(x7)2 + ....+ (x7)6 = 1+x7+x14+....+x42
We will rewrite the above equation, f(x7)=1+(x7−1)+(x14−1)+... + (x42−1)+6
We know that x7−1=(x−1)(x6+x5+...1)
Now It is clear that x7−1 is exactly divisible by f(x).
Also x14−1=(x7)2−12 and x7−1 is a factor of this expression.  (∵xn−an is always divisible by x−a
Similarly, we write x21−1=(x7)3−13, x28−1=(x7)4−14....
So remainder = 1 + 6 = 7
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TCS... Latest papers with solutions - Part1

1. The figure shown can be folded into the shape of a cube.  In the resulting cube, which of the lettered faces is opposite the face marked x?

a. c
b. a
c. d
d. b
Ans: C
Explanation: If you fold the above picture at the dotted lines, X and C are opposite to each other.



2. In how many ways a team of 11 must be selected from 5  men and 11 women such that the team must comprise of not more than 3 men?
a. 1565
b. 1243
c. 2256
d. 2456
Ans: C
Explanation;
The team may consist of 0 men + 11 women, 1 men + 10 women, 2 men + 9 women, or 3 men + 8 women.
So Number of ways are = 11C11+5C1×11C10+5C2×11C9+5C3×11C8 = 2256

3. Given that 0 < a < b < c < d, which of the following the largest ?
a.(c+d) / (a+b)
b.(a+d) / (b+c)
c.(b+c) / (a+d)
d.(b+d) / (a+c)
Sol: A
Explanation: Take a = 1, b = 2, c = 3, d = 4. option A is clearly true.

4. Eesha bought 18 sharpeners for Rs.100.  She paid 1 rupee more for each white sharpener than for each brown sharpener.  What is the price of a white sharpener and how many white sharpener did she buy ?
a. Rs.5, 10
b. Rs.6, 10
c. Rs.5, 8
d. Rs.6, 8
Sol: B
Explanation: Just check the options. If she bought 10 white sharpeners at Rs.6 per piece, She has spent Rs.60 already. And with the remaining Rs.40, she bought 8 brown sharpeners at 40/8 = Rs.5 which is Rs.1 less than White sharpener.

5.

The fourteen digits of a credit card are to be written in the boxes shown above.  If the sum of every three consecutive digits is 18, then the value of x is :
a. 3
b. cannot be determined from the given information.
c. 2
d. 1
Sol : A
Explanation:
Let us assume right most two squares are a , b
Then Sum of all the squares = 18 x 4 + a + b .......... (1)
Also Sum of the squares before 7 = 18
Sum of the squares between 7, x = 18
and sum of the squares between x , 8 = 18
So  Sum of the 14 squares = 18 + 7 + 18 + x + 18  + 8 + a + b (2)
Equating 1 and 2 we get x = 3

6. Four people each roll a four die once.  Find the probability that at least two people will roll the same number ?
a. 5/18
b. 13/18
c. None of the given choices
d. 1295/1296
Sol: B
Explanation:
The number of ways of rolling a dice where no two numbers probability that no one rolls the same number = 6 x 5 x 4 x 3
Now total possibilities of rolling a dice = 64
The probability that a no one gets the same number = 6×5×4×364=518
So the probability that at least two people gets same number = 1−518=1318

7. Jake can dig a well in 16 days.  Paul can dig the same well in 24 days.  Jake, Paul and Hari together dig the well in 8 days.  Hari alone can dig the well in
a. 96 days
b. 48 days
c. 32 days
d. 24 days
Sol:
Explanation: Simple one. Let the total work to be done is 48 meters. Now Jake can dig 3 mts, Paul can dig 2 mts a day. Now all of them combined dug in 8 days so per day they dug 48/8 = 6 mts. So Of these 8 mts, Hari capacity is 1 mt.
So he takes 48 /1 = 48 days to complete the digging job.

Updated : 

8. Eesha bought 18 sharpeners for Rs.100.  She paid 1 rupee more for each white sharpener than for each brown sharpener.  What is the price of a white sharpener and how many white sharpener did she buy ?
a. Rs.5, 10
b. Rs.6, 10
c. Rs.5, 8
d. Rs.6, 8
Ans:
Explanation: This question can be solved easily by going through options.
A. White sharpener total cost: Rs.5 x 10 = Rs.50.  Brown sharpeners cost = Rs.4 x 8 = 32. Total cost is only Rs.82. Wrong option.
B. White sharpener total cost: Rs.6 x 10 = Rs.60.  Brown sharpeners cost = Rs.5 x 8 = 40. Total cost is Rs.100. Correct option.

9. The sum of the digits of a three digit number is 17, and the sum of the squares of its digits is 109.  If we subtract 495 from the number, we shall get a number consisting of the same digits written in the reverse order.  Find the number.
a. 773
b. 683
c. 944
d. 863
Ans: D
Explanation: Check options.  Sum of the squares should be equal to 109. Only Options B and D satisfying. When we subtract 495, only 863 becomes 368.

10. Mark told John "If you give me half your money I will have Rs.75.  John said, "if you give me one third of your money, I will have Rs.75/-  How much money did John have ?
a. 45
b. 60
c. 48
d. 37.5
Ans: B
Explanation: Let the money with Mark and John are M and J respectively.
Now
M + J/2 = 75
M/3 + J = 75
Solving we get M = 45, and J = 60.

11. Eesha has a wheat business.  She purchases wheat from a local wholesaler of a particular cost per pound.  The price of the wheat of her stores is $3 per kg.  Her faulty spring balance reads 0.9 kg for a KG.  Also in the festival season, she gives a 10% discount on the wheat.  She found that she made neither a profit nor a loss in the festival season.  At what price did Eesha purchase the wheat from the wholesaler ?
a. 3
b. 2.5
c. 2.43
d. 2.7
Ans: C
Explanation: Faulty spring balance reads 0.9 kg for a kg" means that she sells 1 kg for the price of 0.9 kgs, so she looses 10% of the price because of the faulty spring balance.  She looses another 10% because of the discount.
So, she actually sells 1 kg for $3×0.9×0.9=$2.43 and since at that price she made neither a profit nor a loss, then Eesha purchase the wheat from the wholesaler for $2.43.

12. Raj goes to market to buy oranges.  If he can bargain and reduce the price per orange by Rs.2, he can buy 30 oranges instead of 20 oranges with the money he has.  How much money does he have ?
a. Rs.100
b. Rs.50
c. Rs.150
d. Rs.120
Ans: D
Explanation: Let the money with Raj is M.  So M20−M30=2.  Check options.  Option D satisfies.

13. A city in the US has a basketball league with three basketball teams, the Aziecs, the Braves and the Celtics.  A sports writer notices that the tallest player of the Aziecs is shorter than the shortest player of the Braves.  The shortest of the Celtics is shorter than the shortest of the Aziecs, while the tallest of the Braves is shorter than the tallest of the Celtics.  The tallest of the Braves is taller than the tallest of the Aziecs.
Which of the following can be judged with certainty ?

X) Paul, a Brave is taller than David, an Aziec
Y) David, a Celtic, is shorter than Edward, an Aziec

a. Both X and Y
b. X only
c. Y only
d. Neither X nor Y
Ans: B
Sol: We solve this problem by taking numbers. Let the shortest of Braves is 4 feet.  Then tallest of Aziecs is less than 4. So let it be 3 feet.
A ->  2 - 3
B -> 4 - 6
C -> 1 - 7
From the above we can safely conclude X is correct. but Y cannot be determined.

14. There are 3 classes having 20, 24 and 30 students respectively having average marks in 
an examination as 20,25 and 30 respectively.  The three classes are represented by A, B and C and you have the following information about the three classes.
a. In class A highest score is 22 and lowest score is 18
b. In class B highest score is 31 and lowest score is 23
c. In class C highest score is 33 and lowest score is 26.

If five students are transferred from A to B, what can be said about the average score of A; and what will happen to the average score of C in a transfer of 5 students from B to C ?
a. definite decrease in both cases
b. can't be determined in both cases
c. definite increase in both cases
d. will remain constant in both cases
Ans: B
Explanation:
Class A average is 20. And their range is 18 to 22
Class B average is 25. And their range is 23 to 31
Class A average is 30. And their range is 26 to 33
If 5 students transferred from A to B, A's average cannot be determined but B's average comes down as the highest score of A is less than lowest score of B.
If 5 students transferred from B to C, C's average cannot be determined the B's range fo marks and C's range of  marks are overlapping.

15. The value of a scooter depreciates in such a way that its value of the end of each year is 3/4 of its value of the beginning of the same year.  If the initial value of the scooter is Rs.40,000, what is the value at the end of 3 years ?
a. Rs.13435
b. Rs.23125
c. Rs.19000
d. Rs.16875
Ans: D
Explanation: 40,000(34)3=16875

16. Rajiv can do a piece of work in 10 days , Venky in 12 days and Ravi in 15 days.  They all start the work together, but Rajiv leaves after 2 days and Venky leaves 3 days before the work is completed.  In how many days is the work completed ?
a. 5
b. 6
c. 9
d. 7
Ans: D
Explanation: Let the work be 60 units. If venky worked for 3 days, and the remaining days of work be x days, total days to complete the work be x + 3 days.
Now Capacities of Rajiv is 60/10 = 6, Venky is 5, Ravi is 4.
(6 + 5 + 4) 2 + (5 + 4) (x - 3) + 5 x 3 = 60.
Solving we get x = 4. So total days to complete the work is 7 days.

17. A man has a job, which requires him to work 8 straight days and rest on the ninth day.  If he started work on Monday, find the day of the week on which he gets his 12th rest day.
a. Thursday
b. Wednesday
c. Tuesday
d. Friday
Ans: B
Explanation:
He works for 8 days and takes rest on the 9th day. So On the 12th rest day, there are 9 x 12 = 108 days passed. Number of odd days = (108 - 1) / 7 = 107 / 7 = 2. So the 12th rest day is wednesday.

18. On a 26 question test, five points were deducted for each wrong answer and eight points were added for each correct answer.  If all the questions were answered, how many were correct, if the score was zero ?
a. 10
b. 12
c. 11
d. 13
Ans: A
Explanation:
Take options and check. If 10 are correct, his score is 10 x 8 = 80.  But 16 are wrong. So total negative marking is 16 x 5 = 80. So final score is zero.