TCS - 2015 Questions-1

TCS – 2015 Questions - 1

1.       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)
Ans: (a)

These type of questions are best answered by apportioning values to the four alphabets.

Let ‘a’ be equal to 1, ‘b’ 2, ‘c’ 3 and ‘d’ 4. Apportioning these values we observe that option (a) is the largest.

2.        

           *       *     *     7     *       *      *      X     *      *      *       8      *       *

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
Ans: (a)

The sum of each three squares is 18. Starting from the left we have four sets of three squares.

Let the last two squares be A and B.

Now we have the total sum of all the squares as -> 18*4 + A + B -> 72 + A + B ………. (i)

Excluding the squares having digits 7, X and 8 we have three sets of three squares.

The total sum of these squares is -> 3*18 + 7 + X + 8 + A + B -> 69 + X + A + B ……….. (ii)

Solving (i) and (ii) we get the value of ‘X’ as 3.

3.       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
Ans: (b)

Jake in one day can do 1/16 work. In 8 days he can do 8/16 -> ½ work

Paul in one day can do 1/24 work. In 8 days he can do 8/24 -> 1/3 work.

Hari in one day can do 1/H work and in 8 days can do 8/H work.

Thus we have an equation :  ½ + 1/3 + 8/H = 1

8/H = 1 – (1/2 + 1/3).  8/H = 1/6  ->  H = 48. Thus Hari will take 48 days to complete the work.

4.       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)

The two points to note here are (i) the sum of the squares is 109 and (ii) and after subtracting 495 the digits are the same in the reverse order. Hence, we can answer this question from the options given.

Only option (b) and (d) fulfil the first condition. But, option (ii) fulfils both the conditions.

Hence the answer is (d) 863. 

5.       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)

Let M and J be the initial money that the two have.

We now have two equations:  

M + J/2 = 75 => 2M + J = 150 …….. (i)

M/3 + J = 75 => M + 3J = 225 …….. (ii)

Multiplying (ii) by 2 we get -> 2M + 6J = 450 …….. (iii)

Subtracting (i) from (iii) we get 5J = 300 and J = 60

6.       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)

Since her spring balance is faulty sale of 1 kg is shown as 0.9kg and thus she loses 10% on the sale price and gets only Rs 2.70 per kg.

Further, she allows additional 10% discount on this price and thus she gets only Rs 2.43 per kg.

At this price there is no gain or loss for her. Hence her purchase price is Rs 2.43 per kg.

7.       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)

Let M be the money that Raj has. Then we have an equation

M/20 – M/30 = 2.  Solving we get the value of M as Rs 120.

8.       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)

Let us take the height of the shortest of the Braves as 4 ft. Then the tallest of the Aziecs is less than these heights say 3 ft. Now we can arrive at the range of heights of the three teams.

Aziecs  height range from 2 – 3

Braves height range from 4 – 6

Celtics height range from 1 – 7

We can now conclude that X is correct while Y cannot be determined.

9.       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.
(i) In class A highest score is 22 and lowest score is 18
(ii) In class B highest score is 31 and lowest score is 23
(iii) 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)
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 of marks and C's range of marks are overlapping.

10.   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)
40000 * (3/4)³ = 16875.