Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 2

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What will be the remainder when $1212121212 \dots 300$ times is being divided by $99$ ?

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Important Questions on Numbers and Their Properties

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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 3

Two players A and B are playing a game of putting '

+

' and '

-

' signs in between any two integers written from

1

to

100

. A starts the game by placing

a + sign

anywhere between any two integers. Once all the signs have been placed, the result is calculated. If it is even, then A wins and if it is odd, then B wins, provided they are placing signs by taking turns one by one and either of them can place any sign anywhere between any two integers. Who will win at the end?

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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 4

What is the remainder when

2^{100}

is divided by

101 ?

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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 5

If

S = \{X_{1}, X_{2}, X_{3}, \dots X_{n}\}

, where

n > 0, X_{1} = 1

is a set of positive numbers where

X = X_{n - 1} + 2^{n} - 1

. Which of the following sets of numbers does S resemble?

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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 6

A three-digit number ABC is a perfect square and the number of factors of this number is also a perfect square. If

(A + B + C)

is also a perfect square, then what is the number of factors of the six-digit number ABCABC?

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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 7

How many divisors of

10^{5}

will have at least one zero at its end?

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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 8

Let

V_{1}, V_{2}, V_{3}, \dots, V_{100}

be hundred positive integers such that

V_{i} + V_{i + 1} + V_{i + 2} + V_{i + 3} = K

, where K is a constant and

i = 1, 2, 3, \dots, 97

. If

V_{3} = 9

, then what is the value of

V_{99}

?

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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 9

In the abovementioned question, if

V_{5} = 7

, then what is the value of

V_{90}

?

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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 10

What is the largest integer that is a divisor of

(n + 1) (n + 3) (n + 5) (n + 7) (n + 9)

for all positive even integers n?