How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 171

MEDIUM

CAT

IMPORTANT

Earn 100

if $x$ is a natural number and $4 < x < 50$ , then the largest $n$ , such that $n!$ would always divide $x (x^{2} - 1) (x^{2} - 4) (x^{2} - 9) (x + 4)$ is?

50% studentsanswered this correctly

Important Questions on Number Systems

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 172

if

X

is a natural number and

X!

ends with

Y

zeroes then the number of zeroes at the end of

5 X!

is:

HARD

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 173

There are

90

questions in a test. Each correct answer fetches

1

mark, each wrong answer and unanswered question attract a penalty of

\frac{1}{4}

marks and

\frac{1}{8}

marks respectively. Bilbo scored

23

marks in the test. What is the minimum possible number of the questions wrongly answered by him?

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 174

If

A = {n^{2 n}}^{n}, B = n^{n^{2 n}}, C = {(n^{2 n})}^{n}, D = {(n^{n})}^{n^{2}}

when

n

is a natural number and

n \neq 1

. Then arrange them in terms of their values.

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 175

How many numbers in the form of $(2^{n} - 1)$ which are less than $5000$ are prime?

HARD

CAT

IMPORTANT

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

The arithmetic mean of two numbers is smaller by

24

than the larger of two numbers and the GM of the same two numbers exceeds by

12

the smaller of the numbers. Find the numbers.

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 2

Find the number of numbers between

200

and

300

, both included, which are not divisible by

2, 3, 4

and

5

.

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 3

Given

x

and

n

are integers,

(15 n^{3} + 6 n^{2} + 5 n + x) / n

is not an integer for what condition?

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 4

The unit digit in the expression

36^{234} \times 33^{512} \times 39^{180} - 54^{29} \times 25^{123} \times 31^{512}

will be: