# CAT Questions | CAT Number System Questions

###### CAT Quantitative Aptitude | CAT Number theory: Factors problems

A CAT Number theory question that appears in the Quantitative Aptitude section of the CAT Exam broadly tests an aspirant on the concepts - Factors, Factorials, HCF and LCM, base system & remainders of the above mentioned concepts. In CAT Exam, one can generally expect to get 1 question from CAT Number Systems involving Factors.CAT Quantitiative Aptitude questions from Factors involve ideas like Sum of Factors, Odd factors, Even Factors and so on. CAT Number Systems is an important topic with lots of weightage in the CAT Exam. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

1. #### CAT Number Systems - Factors

The sum of the factors of a number is 124. What is the number?

1. Number lies between 40 and 50
2. Number lies between 50 and 60
3. Number lies between 60 and 80
4. More than one such number exists

2. #### CAT Number Systems - Factors

How many factors of 1080 are perfect squares?

1. 4
2. 6
3. 8
4. 5

3. #### CAT Number Systems - Factors

How many factors of 25 * 36 * 52 are perfect squares?

1. 18
2. 24
3. 36
4. 8

4. #### CAT Number Systems - Odd Factors

How many factors of 24 * 53 * 74 are odd numbers?

1. 100
2. 99
3. 20
4. 24

5. #### CAT Number Systems - Factors

How many factors of the number 28 * 36 * 54 * 105 are multiples of 120?

1. 540
2. 660
3. 594
4. 792

6. #### CAT Number Systems - Even Factors

Number N = 26 * 55 * 76 * 107; how many factors of N are even numbers?

1. 1183
2. 1200
3. 1050
4. 840

7. #### CAT Number Systems - Perfect Cube

Numbers A, B, C and D have 16, 28, 30 and 27 factors. Which of these could be a perfect cube?

1. A and B
2. B and C
3. A, B and C
4. B and D

8. #### CAT Number Theory 'abcabc'

If a three digit number ‘abc’ has 3 factors, how many factors does the 6-digit number ‘abcabc’ have?

1. 16 factors
2. 24 factors
3. 16 or 24 factors
4. 20 factors

9. #### CAT Number Systems - Brute Force

How many numbers are there less than 100 that cannot be written as a multiple of a perfect square greater than 1?

1. 61
2. 56
3. 52
4. 65

10. #### CAT Number Systems - 18 factors

Find the smallest number that has exactly 18 factors.

1. 180
2. 216
3. 240
4. None of these

11. #### CAT Number Systems - Factors

A number N2 has 15 factors. How many factors can N have?

1. 5 or 7 factors
2. 6 or 8 factors
3. 4 or 6 factors
4. 9 or 8 factors

12. #### CAT Number Theory 'abcabc'

If a three digit number ‘abc’ has 2 factors (where a, b, c are digits), how many factors does the 6-digit number ‘abcabc’ have?

1. 16
2. 24
3. 18
4. 30

13. #### CAT Number Systems - 12 Factors

What is the smallest number that has exactly 12 factors?

1. 211
2. 60
3. 120
4. 144

The Questions that follow, are from actual CAT papers. If you wish to take them separately or plan to solve actual CAT papers at a later point in time, It would be a good idea to stop here.

1. #### CAT 2022 Slot 3 - QA

If $$c=\frac{16 x}{y}+\frac{49 y}{x}$$ for some non-zero real numbers $$x$$ and $$y$$, then $$c$$ cannot take the value

1. -70
2. 60
3. -50
4. -60

2. #### CAT 2020 Question Paper Slot 3 - Number Theory

How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

1. 41
2. 42
3. 40
4. 43

3. #### CAT 2020 Question Paper Slot 3 - Digits

Let m and n be natural numbers such that n is even and 0.2 < \\frac{m}{20}), \\frac{n}{m}), \\frac{n}{11}) < 0.5. Then m - 2n equals

1. 4
2. 2
3. 1
4. 3

4. #### CAT 2019 Question Paper Slot 2 - Number theory

How many factors of 24 × 35 × 104 are perfect squares which are greater than 1? [TITA]

1. #### CAT 2018 Question Paper Slot 2 - Number Theory

If N and x are positive integers such that NN = 2160 and N2 + 2N is an integral multiple of 2x, then the largest possible x is (TITA)

1. #### CAT 2018 Question Paper Slot 1 - Number Theory

The number of integers x such that 0.25 < 2x < 200, and 2x + 2 is perfectly divisible by either 3 or 4, is [TITA]

The Questions that follow, are from actual XAT papers. If you wish to take them separately or plan to solve actual XAT papers at a later point in time, It would be a good idea to stop here.

1. #### XAT 2019 Question Paper - QADI

Two numbers a and b are inversely proportional to each other. If a increases by 100%, then b decreases by:

1. 200%
2. 100%
3. 150%
4. 80%
5. 50%

The Questions that follow, are from actual IPMAT papers. If you wish to take them separately or plan to solve actual IPMAT papers at a later point in time, It would be a good idea to stop here.

1. #### IPMAT 2020 Question Paper - IPM Indore Quants

In a class, students are assigned roll numbers from 1 to 140. All students with even roll numbers opted for cricket, all those whose roll numbers are divisible by 5 opted for football, and all those whose roll numbers are divisible by 3 opted for basketball. 'The number of students who did not opt for any of the three sports is

1. 102
2. 38
3. 98
4. 42

2. #### IPMAT 2019 Question Paper - IPM Indore Quants

You have been asked to select a positive integer N which is less than 1000 , such that it is either a multiple of 4, or a multiple of 6, or an odd multiple of 9. The number of such numbers is

3. #### IPMAT 2019 Question Paper - IPM Indore Quants

Placing which of the following two digits at the right end of 4530 makes the resultant six digit number divisible by 6,7 and 9?

1. 96
2. 78
3. 42
4. 54

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