Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 14

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CAT

IMPORTANT

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If a, b and c are $3$ consecutive integers between $- 10$ to $+ 10$ (both inclusive), how many integer values are possible for the expression: $\frac{(a^{3} + b^{3} + c^{3} + 3 abc)}{(a + b + c)^{2}}$ ?

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Important Questions on Numbers and Their Properties

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CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 15

What is the sum of integer

54

through

196

inclusive?

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CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 16

The highest number amongst

\sqrt{2}, \sqrt[3]{3}

, and

\sqrt[4]{4}

is:

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CAT

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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 17

If

a, b, c, d

are four different positive integers selected from 1 to 25 then the highest possible value of

\frac{[(a + b) + (c + d)]}{[(a + b) + (c - d)]}

would be :

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CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 18

A three-digit number has digits in strictly descending order and divisible by

10

. By changing the places of the digits a new three-digit number is constructed in such a way that the new number is also divisible by

10

. The difference between the original number and the new number is divisible by

40

. How many numbers will satisfy all these conditions?

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CAT

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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 19

The integers

1, 2, . . ., 40

are written on a blackboard. The following operation is then repeated

39

times: in each repetition, any two numbers say

a and b

, currently on the blackboard are erased and a new number

a + b - 1

is written. What will be the number left on the board at the end?

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CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 20

What are the last two digits of

7^{2008}

?

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CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 21

How many pairs of positive integers

m, n

satisfy

\frac{1}{m} + \frac{4}{n} = \frac{1}{12}

where n is an odd integer less than

60 ?

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 22

Consider four digit numbers for which the first two digits are equal and last two digits are also equal. How many such numbers are perfect squares?