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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.

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
Choice D
More than one such number exists.
CAT Number Systems - Factors

How many factors of 1080 are perfect squares?
1. 4
2. 6
3. 8
4. 5
Choice A
4
CAT Number Systems - Factors

How many factors of 2⁵ * 3⁶ * 5² are perfect squares?
1. 18
2. 24
3. 36
4. 8
Choice B
24
CAT Number Systems - Odd Factors

How many factors of 2⁴ * 5³ * 7⁴ are odd numbers?
1. 100
2. 99
3. 20
4. 24
Choice C
20
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
Choice C
594
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
Choice A
1183
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
Choice A
A and B
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
Choice C
16 or 24 factors
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
Choice A
61
CAT Number Systems - 18 factors

Find the smallest number that has exactly 18 factors.
1. 180
2. 216
3. 240
4. None of these
Choice A
180
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
Choice B
6 or 8 factors
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
Choice A
16
CAT Number Systems - 12 Factors

What is the smallest number that has exactly 12 factors?
1. 211
2. 60
3. 120
4. 144
Choice B
60

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.

CAT 2023 Slot 3 - QA
The sum of the first two natural numbers, each having 15 factors (including 1 and the number itself), is
468
CAT 2023 Slot 2 - QA
For any natural numbers \(m, n\), and \(k\), such that \(k\) divides both \(m+2 n\) and \(3 m+4 n, k\) must be a common divisor of
1. \(2 m\) and \(3 n\)
2. \(m\) and \(2 n\)
3. \(2 m\) and \(n\)
4. \(m\) and \(n\)
Choice B
\(m\) and \(2 n\)
CAT 2023 Slot 2 - QA
The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is
15
CAT 2023 Slot 1 - QA
Let \(n\) be the least positive integer such that 168 is a factor of \(1134^n\). If \(m\) is the least positive integer such that \(1134^n\) is a factor of \(168^m\), then \(m+n\) equals
1. 12
2. 9
3. 15
4. 24
Choice C
15
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
Choice C
-50
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
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
CAT 2019 Question Paper Slot 2 - Number theory
How many factors of 2⁴ × 3⁵ × 10⁴ are perfect squares which are greater than 1? [TITA]
44
CAT 2019 Question Paper Slot 2 - Number theory
How many pairs (m,n) of positive integers satisfy the equation the equation m² + 105 = n²? [TITA]
4
CAT 2018 Question Paper Slot 2 - Number Theory
If N and x are positive integers such that N^N = 2¹⁶⁰ and N² + 2^N is an integral multiple of 2^x, then the largest possible x is (TITA)
10
CAT 2018 Question Paper Slot 1 - Number Theory
The number of integers x such that 0.25 < 2^x < 200, and 2^x + 2 is perfectly divisible by either 3 or 4, is [TITA]
5

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.

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%
Choice E
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.

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
Choice B
38
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
388
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
Choice A
96