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

EASY

CAT

IMPORTANT

Earn 100

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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Important Questions on Number Systems

MEDIUM

CAT

IMPORTANT

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}

?

EASY

CAT

IMPORTANT

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?

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 114

Three natural numbers

X, Y, Z

are prime numbers less than

20

are in arithmetic progression. If

X > Y > Z

, then how many possible values can we get for

X + Y + Z

?

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 115

A

100

- digit number is multiplied by a

200

- digit number and the product is multiplied with a

300

digit number and this product is again multiplied with a

400

digits number. What is the least number of digits in the product?

MEDIUM

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 116

What are the last two digits of the number

3^{400}

?

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 117

The unit digit in

1^{7} \times 2^{7} \times 3^{7} \times . . . . . \times 9^{7} \times 11^{7} \times 12^{7} \times . . . . . \times 19^{7} \times 21^{7} . . . . . \times 99^{7}

is

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 118

How many two digit numbers have their squares as

1

more than a multiple of

24

?

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 119

There are

80

questions in a test. Each correct answer fetches

1

mark, each wrong answer and unanswered question attract penalty of

\frac{1}{4}

mark and

\frac{1}{8}

mark respectively each. Frodo scored

23

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