CAT 2001 — QA Question 38

Change in AverageEasy

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 = $\frac{r_{1} + r_{2}}{n_{1}}$

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

MBA₁ = $\frac{r_{1}}{n_{1}} + \frac{n_{2}}{n_{1}} \times m a x [0, (\frac{r_{2}}{n_{2}} - \frac{r_{1}}{n_{1}}])$

MBA₂ = $\frac{r_{1} + r_{2}}{n_{1} + n_{2}}$

An experienced cricketer with no incomplete innings has a BA of 50. The next time he bats, the innings is incomplete and he scores 45 runs. It can be inferred that:

Answer & solution

A
BA and MBA₁ will both increase
BA will increase and MBA₂ will decrease
C
BA will increase and not enough data is available to assess change in MBA₁and MBA₂
D
None of these

Solution

As 45 is less than his current average of 50, MBA₂ goes down. But with any incomplete innings, BA increases.

Hence, option (b).

CAT 2001 QA Q38: An experienced cricketer with no incomplete innings has a BA of 50. The next time he bats, the innings is inco — Solution | TheCATExam