TheCATExam
Sign in

CAT 2001 — QA Question 39

Basics of QuadrilateralsEasy
Passage / Data

Answer the following question based on the information given below.

The batting average (BA) of a test batsman is computed from runs scored and innings played-completed innings and incomplete innings (not out) in the following manner:

r1 = number of runs scored in completed innings; n1 = number of completed innings

r2 = number of runs scored in incomplete innings; n2 = number of incomplete innings

BA = r1+r2n1

To better assess batsman's accomplishments, the ICC is considering two other measures MBA1 and MBA2 defined as follows:

MBA1 = r1n1+n2n1× max[0, (r2n2-r1n1])

MBA2 = r1+r2n1+n2

Based on the figure below, what is the value of x, if y = 10?

Answer & solution

  • A

    0

  • 11

  • C

    12

  • D

    None of these

Solution

The third side of the triangle with sides 10 and x - 3 is 100-(x-3)2

∴ In the large triangle,

(x - 3)2 + (x + 4)2 = [x+100-(x-3)2]2

Only x = 11 satisfies this equation

Hence, option (b).

Alternatively,

x – 3 and x + 4 form part of a Pythagorean triplet. x = 12 and x = 10 does not give a Pythagorean triplet. With x = 11, we have 8, 15, 17.

This means that the large triangle has a hypotenuse of 17.

Therefore, one side of the smallest triangle is 17 – x = 17 – 11 = 6

As 6, 8, and 10 form a Pythagorean triplet, x is definitely equal to 11.

CAT 2001 QA Q39: Based on the figure below, what is the value of x, if y = 10? — Solution | TheCATExam