CAT Questions | CAT Number Systems 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. In CAT Exam, one can generally expect a few questions from CAT Number Systems. CAT Number Systems is an important topic in the CAT Exam. Inside this vast topic, Factorials is tested frequently. You can expect approx 1 question involving CAT factorials. As an aside, Factorials is also useful in CAT Permutation and Combination. 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 FACTORIAL BASE 6 BASE 8 MATH

   A number n! is written in base 6 and base 8 notation. Its base 6 representation ends with 10 zeroes. Its base 8 representation ends with 7 zeroes. Find the smallest n that satisfies these conditions. Also find the number of values of n that will satisfy these conditions.

   1. 22 and 4
   2. 32 and 2
   3. 24 and 3
   4. 25 and 4

   Correct AnswerChoice C
   24 and 3

   Explanation

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2. CAT Factorial, factors

   Given N is a positive integer less than 31, how many values can n take if (n + 1) is a factor of n!?

   1. 18
   2. 16
   3. 12
   4. 20

   Correct AnswerChoice A
   18

   Explanation

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3. CAT Factorials - basic

   How many values can natural number n take, if n! is a multiple of 7⁶ but not 7⁹?

   1. 7
   2. 21
   3. 14
   4. 12

   Correct AnswerChoice C
   14

   Explanation

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4. CAT Factorials - basic

   How many values can natural number n take, if n! is a multiple of 2²⁰ but not 3²⁰?

   1. 11
   2. 21
   3. 16
   4. 5

   Correct AnswerChoice B
   21

   Explanation

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5. CAT Factorials - Trailing zeroes

   How many trailing zeroes (zeroes at the end of the number) does 60! have?

   1. 14
   2. 12
   3. 10
   4. 8

   Correct AnswerChoice A
   14

   Explanation

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6. CAT Factorials - basic

   What is the highest power of 12 that divides 54!?

   1. 25
   2. 26
   3. 30
   4. 4

   Correct AnswerChoice A
   25

   Explanation

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7. Factorials - Trailing zeroes

   Find the least number n such that no factorial has n trailing zeroes, or n + 1 trailing zeroes or n + 2 trailing zeroes.

   1. 153
   2. 126
   3. 624
   4. 18

   Correct AnswerChoice A
   153

   Explanation

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8. CAT Factorials - base 8

   When 40! is expressed in base 8 form, what is the last non–zero digit in the base 8 expansion?

   1. 2
   2. 6
   3. 4
   4. 2 or 6

   Correct AnswerChoice C
   4

   Explanation Video Solution

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9. CAT Factorials and Factors

   Let K be the largest number with exactly 3 factors that divide 25! How many factors does (k – 1) have?

   1. 16
   2. 12
   3. 9
   4. 14

   Correct AnswerChoice A
   16

   Explanation Video Solution

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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.

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1. CAT 2022 Slot 2 - QA

   For some natural number \(n\), assume that \((15,000)\) ! is divisible by \((n !) !\). The largest possible value of \(n\) is

   1. 5
   2. 7
   3. 4
   4. 6

   Correct AnswerChoice B
   7

   Video ExplanationExplanation

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