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

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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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Important Questions on Number Systems

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

If

[\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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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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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

in

M

.

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 110

x and y

are natural numbers such that they satisfy the equation

x + y + 21 = 3 x y

. Find the maximum possible integral power of

6 in (x y)! . [n! is the product of first' n' natural numbers.]

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 111

Let

X

is the set of all the natural numbers each of which is equal to the number of its factors

& Y

is the set of all natural numbers from

1 to 100

, each of which differ from the sum of its factors by

1

. Also, let

x & y

represent the number of elements in the sets respectively. Then find the value of

[\frac{y}{x}]

where

[]

represents the greatest integer function.

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 112

A four digit number

X

has

15

factors. What is the number of factors of

X^{2}

?

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 113

How many four-digit odd numbers are possible such that the hundreds digit is two more than the tens digit?