CAT 2001 — QA Question 43
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 =
To better assess batsman's accomplishments, the ICC is considering two other measures MBA1 and MBA2 defined as follows:
MBA1 =
MBA2 =
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
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).