CAT Questions | CAT Number System Questions

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

   Correct AnswerChoice D
   More than one such number exists.

   Explanation

   ---

2. CAT Number Systems - Factors

   How many factors of 1080 are perfect squares?

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

   Correct AnswerChoice A
   4

   Explanation

   ---

3. CAT Number Systems - Factors

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

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

   Correct AnswerChoice B
   24

   Explanation

   ---

4. CAT Number Systems - Odd Factors

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

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

   Correct AnswerChoice C
   20

   Explanation

   ---

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

   Correct AnswerChoice C
   594

   Explanation

   ---

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

   Correct AnswerChoice A
   1183

   Explanation

   ---

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

   Correct AnswerChoice A
   A and B

   Explanation

   ---

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

   Correct AnswerChoice C
   16 or 24 factors

   Explanation

   ---

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

   Correct AnswerChoice A
   61

   Explanation

   ---

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

    Correct AnswerChoice A
    180

    Explanation

    ---

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

    Correct AnswerChoice B
    6 or 8 factors

    Explanation

    ---

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

    Correct AnswerChoice A
    16

    Explanation

    ---

13. CAT Number Systems - 12 Factors

    What is the smallest number that has exactly 12 factors?

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

    Correct AnswerChoice B
    60

    Explanation Video Solution

    ---

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

   Correct AnswerChoice C
   -50

   Video ExplanationExplanation

   ---

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

   Correct AnswerChoice A
   41

   Video SolutionExplanation

   ---

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

   Correct AnswerChoice C
   1

   Video SolutionExplanation

   ---

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]

   Correct Answer44
   

   ExplanationVideo Solution

   ---

5. 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)

   Correct Answer10
   

   ExplanationVideo Solution

   ---

6. 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]

   Correct Answer5
   

   ExplanationVideo Solution

   ---

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%

   Correct AnswerChoice E
   50%

   Video SolutionExplanation

   ---

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

   Correct AnswerChoice B
   38

   Explanation

   ---

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

   Correct Answer388

   ExplanationVideo Solution

   ---

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

   Correct AnswerChoice A
   96

   ExplanationVideo Solution

   ---