CAT 2001 — QA Question 37

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

Based on the information provided which of the following is true?

Answer & solution

A
MBA₁ ≤ BA ≤ MBA₂
B
BA ≤ MBA₂ ≤ MBA₁
C
MBA₂ ≤ BA ≤ MBA₁
None of these

Solution

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

MBA₁ = $\frac{r_{1}}{n_{1}} + \frac{n_{2}}{n_{1}} \times \frac{r_{2} n_{2} - r_{1} n_{2}}{n_{1} n_{2}} = \frac{r_{1}}{n_{1}} + \frac{r_{2}}{n_{1}} - \frac{r_{1} n_{2}}{n_{1}}$

Whatever may be the values, MBA₁ < BA

Similarly, we can observe that MBA₂ ≤ BA

Hence, option (d).

CAT 2001 QA Q37: Based on the information provided which of the following is true? — Solution | TheCATExam