CAT Number System Questions for Practice

Question 1:
A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is $35\frac{7}{{17}}$. What was the number erased?
Topic: Basics

[1] 7
[2] 8
[3] 9
[4] None of these

Question 2:
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?

Topic: Basics

[1] MBA1≤ BA ≤ MBA2
[2] BA ≤ MBA2≤ MBA1
[3] MBA2≤ BA ≤ MBA1
[4] None of these

Question 3:
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

Topic: Basics

[1] BA and MBA1will both increase
[2] BA will increase and MBA2will decrease
[3] BA will increase and not enough data is available to assess change in MBA1and MBA2
[4] None of these

Question 4:
Let b be a positive integer and a = b2– b. If b ≥ 4 , then a2– 2a is divisible by
Topic: Divisibility

[1] 15
[2] 20
[3] 24
[4] All of these