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?

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

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

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

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

[1] 11
[2] 12
[3] 13
[4] None of these
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