Question

The problem below consists of a question and two statements numbered 1 & 2. You have to decide whether the data provided in the statements are sufficient to answer the question.
In a cricket match, three slip fielders are positioned in a straight line. The distance between the 1st slip and the 2nd slip is the same as the distance between the 2nd slip and the 3rd slip. The player X, who is not on the same line of slip fielders, throws a ball to the 3rd slip and the ball takes 5 seconds to reach the player at the 3rd slip. If he had thrown the ball at the same speed to the 1st slip or to the 2nd slip, it would have taken 3 seconds or 4 seconds, respectively. What is the distance between the 2nd slip and player X?
1. The ball travels at a speed of 3.6 km/hour.
2. The distance between the 1st slip and the 3rd slip is 2 meters.

• A. Statement 1 alone is sufficient to answer the question, but statement 2 alone is not sufficient
• B. Statement 2 alone is sufficient to answer the question, but statement 1 alone is not sufficient.
• C. Each statement alone is sufficient.
• D. Both statements together are sufficient, but neither of them alone is sufficient.
• E. Statements 1 & 2 together are not sufficient.

Answer 1

Answer: (E)

Statements 1 & 2 together are not sufficient.

Answer 2

The ball takes 5 seconds, 4 seconds, and 3 seconds, respectively, to reach the 3rd slip, 2nd slip, and 1st slip.
Let the distance between X and 3rd slip, 2nd slip, and 1st slip, respectively, be 5a meters, 4a meters, and 3a meters, and let the distance between 1st and 2nd, 2nd and 3rd slip be ‘d’ meters.
According to the question:

Using the Apollonius theorem,
(5a)2 + (3a)2 = 2(4a)2 + 2(d)2
2a2 = 2d2
or, a = d
But (3a, 2a, 5a) cannot form a triangle and X is not on the same line contradicting each other. Hence, the question is incorrect.