Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 24

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CAT

IMPORTANT

Earn 100

What is the remainder when $3^{450}$ is divided by $108$ ?

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Important Questions on Numbers and Their Properties

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IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 25

P is a natural number.

2 P

has

28

divisors and

3 P

has

30

divisors. How many divisors of

6 P

will be there?

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CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 26

pqr is a three-digit natural number such that

pqr = p^{3} + q^{3} + r^{3} .

What is the value of r?

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CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 27

There are two three-digit numbers. When one number is divided by another number, quotient obtained is

6

and remainder is

0

. The sum total of both the numbers is a multiple of

504

. What is the difference between the numbers?

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IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 28

LCM of

12^{24}, 16^{18}

and

N

is

24^{24} .

Number of all the possible values of

N = S .

What is the value of

S ?

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 29

Each of P, Q, R, and S equals either

0

or

1

. It is given that

If $Q = 0$ , then $R = 1$ ;

If $R = 0$ , then $P = S$ ;

If $S = 0$ , then $P = 1$ ;

Let us assume that

R = 0

, find the value of

(P + Q + R + S)

?

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CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 30

When asked about his date of birth in

1996

, Mayank replied that 'last two digits of my birth year stands for my age.' When Siddharth was asked about his age, he also replied the same. However, Siddharth is older to Mayank. What is the difference in their age?

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IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 36

What is the value of N in the following expression

345_{6} + 632_{7} + 487_{9} = (N)_{5} ?

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CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 37

In a certain system of writing of numbers, we write $(12 Φ)_{4} = (124)_{Φ}$ , where $Φ$ is the units digit in the first place and number of digits in that system in the second place.

How many values of $Φ$ are possible?