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IMPORTANT

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How many two-digit numbers less than or equal to $50$ , have the product of the factorials of their digits less than or equal to the sum of the factorials of their digits?

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Important Questions on Number Systems

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IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 96

A candidate takes a test and attempts all the

100

questions in it. While any correct answer fetches

1

mark, wrong answers are penalised as follows; one-tenth of the questions carry

\frac{1}{10}

negative mark each, one-fifth of the questions carry

\frac{1}{5}

negative marks each and the rest of the questions carry

\frac{1}{2}

negative mark each. Unattempted questions carry no marks. What is the difference between the maximum and the minimum marks that he can score?

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 100

Amitabh has a certain number of toffees, such that if he distributes them amongst ten children he has nine left, if he distributes amongst

9

children he would have

8

left, if he distributes amongst

8

children he would have

7

left ... and so on until if he distributes amongst

5

children he should have

4

left. What is the second lowest number of toffees he could have with him?

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 101

If a positive integer

' n'

is subtracted from the squares of three consecutive terms of an Arithmetic Progression, the numbers obtained are

108, 220 and 364

respectively. What is the sum of the digits of

' n'

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CAT

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 102

How many integers exist such that not only are they multiples of

904^{2008}

but also are factors of

904^{2015}

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 103

What is the remainder when

1^{5} + 2^{5} + 3^{5} + . . . + 96^{5}

is divided by

194

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 104

[\frac{s}{2}] + [\frac{s}{3}] + [\frac{s}{7}] = \frac{41}{42} s

where

[s]

is the greatest integer less than or equal to

' s'

and

0 < s < 1000

, then find the number of possible values of

' s'

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 108

Let

A

be a two-digit number. The sum of the number

A

, the number formed by reversing the digits of

A

and the value of the product of the digits of

A

is found to equal

117

. Then what is the sum of the digits of

A

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 109

Let

M

be the product of all natural numbers between

35 and 250

that have an odd number of factors. Find the highest power of

12

M

How many two-digit numbers less than or equal to 50, have the product of the factorials of their digits less than or equal to the sum of the factorials of their digits?

Important Questions on Number Systems

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How many two-digit numbers less than or equal to $50$ , have the product of the factorials of their digits less than or equal to the sum of the factorials of their digits?