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:

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

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

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

BA and MBA1will both increase
BA will increase and MBA2will decrease
BA will increase and not enough data is available to assess change in MBA1and MBA2
None of these
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