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# CAT Number system Practice Problems Set 06

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

 7
 8
 9
 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

 MBA1≤ BA ≤ MBA2
 BA ≤ MBA2≤ MBA1
 MBA2≤ BA ≤ MBA1
 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

 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

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

 15
 20
 24
 All of these

Question 5:
Ashish is given Rs. 158 in one-rupee denominations. He has been asked to allocate them into a number of bags such that any amount required between Re 1 and Rs. 158 can be given by handing out a certain number of bags without opening them. What is the minimum number of bags required?
Topic: Basics

 11
 12
 13
 None of these

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