# CAT Quant Practice Problems

Question: 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

A = $\frac{{{{\rm{r}}_1} + {{\rm{r}}_2}}}{{{{\rm{n}}_{\rm{1}}}}}$

To better assess a batsman’s accomplishments, the ICC is considering two other measures MBA1and MBA2defined as follows:

${\rm{MB}}{{\rm{A}}_1} = \frac{{{r_1}}}{{{n_1}}} + \frac{{{n_2}}}{{n1}}\max \left[ {0,\left( {\frac{{{r_2}}}{{{n_2}}} - \frac{{{r_1}}}{{{n_1}}}} \right)} \right]$

${\rm{MB}}{{\rm{A}}_2} = \frac{{{r_{1 + }}{r_2}}}{{{n_1} + {n_2}}}$

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

 MBA1≤ BA ≤ MBA2 BA ≤ MBA2≤ MBA1 MBA2≤ BA ≤ MBA1 None of these

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