CAT 2001QA Question 43

Number TheoryEasy
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:

MBA1r1n1+n2n1× max[0, (r2n2-r1n1])

MBA2 = r1+r2n1+n2

In some code, letters, a, b, c, d and e represent numbers 2, 4, 5, 6 and 10. However, we don't know which letter represent which number. Consider the following relationships:

i. a + c = e
ii. b – d = d
iii. e + a = b

Answer & solution

  • A

    b = 4, d = 2

  • a = 4, e = 6

  • C

    b = 6, e = 2

  • D

    a = 4, c = 6

Solution

a + c = e              ... (i)

b – d = d

b = 2d                  ... (ii)

e + a = b              ... (iii)

From (ii), we get,

Either b = 4 and d = 2 or b = 10 and d = 5

From (i) and (iii), we get,

2a + c = b            ... (iv)

∴ b = 4 can easily be eliminated because there is no value of b that will satisfy equation (iv).

∴ b = 10 and d = 5

a = 4 or 6 and e = 6 or 4, but c = 2

Using equation (i), we have,

a = 4 and e = 6

Hence, option (b).

CAT 2001 QA Q43: In some code, letters, a, b, c, d and e represent numbers 2, 4, 5, 6 and 10. However, we don't know which lett — Solution | TheCATExam