Interview Questions

Quantitative Aptitude Back

There are 3 persons Sudhir, Arvind, and Gauri. Sudhir lent cars to Arvind and Gauri as many as they had already. After some time Arvind gave as many cars to Sudhir and Gauri as many as they have. After sometime Gauri did the same thing. At the end of this transaction each one of them had 24. Find the cars each originally had.
Ans: 

Sudhir had 39 cars, Arvind had 21 cars and Gauri had 12 cars.

Sudhir Arvind Gauri
Finally 24 24 24
Before Gauri's transaction 12 12 48
Before Arvind's transaction 6 42 24
Before Sudhir' s transaction 39 21 12.

A man bought a horse and a cart. If he sold the horse at 10 % loss and the cart at 20 % gain, he would not lose anything; but if he sold the horse at 5% loss and the cart at 5% gain, he would lose Rs. 10 in the bargain. The amount paid by him was Rs.- _______ for the horse and Rs.________ for the cart.
Ans: 

Cost price of horse: Rs. 400 & Cost price of cart: Rs. 200.

Let x be the cost of horse & y be the cost of the cart.
10 % of loss in selling horse = 20 % of gain in selling the cart
Therefore (10 / 100) * x = (20 * 100) * y
x = 2y -----------(1)
5 % of loss in selling the horse is 10 more than the 5 % gain in selling the cart. Therefore (5 / 100) * x - 10 = (5 / 100) * y
5x - 1000 = 5y
Substituting (1)
10y - 1000 = 5y
5y = 1000
y = 200
x = 400 from (1).

For the following, find the next term in the series 1. 6, 24, 60,120, 210
Ans: 

336.
The series is 1.2.3, 2.3.4, 3.4.5, 4.5.6, 5.6.7, ..... ( '.' means product).

What is the number of zeros at the end of the product of the numbers from 1 to 100?
Ans: 

127.

A fast typist can type some matter in 2 hours and a slow typist can type the same in 3 hours. If both type combinely, in how much time will they finish?
Ans: 

1 hr 12 min.
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 combinely, 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.

Gavaskar's average in his first 50 innings was 50. After the 51st innings, his average was 51. How many runs did he score in his 51st innings. (supposing that he lost his wicket in his 51st innings)
Ans: 

101.
Total score after 50 innings = 50*50 = 2500 Total score after 51 innings = 51*51 = 2601 So, runs made in the 51st innings = 2601-2500 = 101 If he had not lost his wicket in his 51st innings, he would have scored an unbeaten 50 in his 51st innings.

Out of 80 coins, one is counterfeit. What is the minimum number of weighings needed to find out the counterfeit coin?
Ans: 

4.

A rectangular plate with length 8 inches, breadth 11 inches and thickness 2 inches is available. What is the length of the circular rod with diameter 8 inches and equal to the volume of the rectangular plate?
Ans: 

3.5 inches.
Volume of the circular rod (cylinder) = Volume of the rectangular plate (22/7)*4*4*h = 8*11*2, h = 7/2 = 3.5.

What is the sum of all numbers between 100 and 1000 which are divisible by 14 ?
Ans: 

35392.
The number closest to 100 which is greater than 100 and divisible by14 is 112, which is the first term of the series which has to be summed. The number closest to 1000 which is less than 1000 and divisible by 14 is 994,which is the last term of the series.112 + 126 + .... + 994 = 14(8+9+ ... + 71) = 35392.

If s(a) denotes square root of a, find the value of s(12+s(12+s(12+ ...... upto infinity.
Ans: 

4.
Let x = s(12+s(12+s(12+..... ) We can write x = s(12+x). i.e., x^2 = 12 + x. Solving this quadratic equation, we get x = -3 or x=4. Sum cannot be -ve and hence sum = 4.