CAT Practice : Number System: Factorial

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The following topics are covered in the CAT quant section from Number system - Factorial. Detailed explanatory answers, solution videos and slide decks are also provided.
  1. 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
      Correct answer
    • Explanatory Answer
    • Different bases and factorial
    • Hard
  2. 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
      Correct answer
    • Explanatory Answer
    • Factorial, factors, primes
    • Hard
  3. 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
  4. 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
  5. 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
  6. Factorials - basic

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

    1. 25
    2. 26
    3. 30
    4. 4
  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
  8. 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
      Correct answer
    • Explanatory Answer
    • Factorials and octal system
    • Hard
  9. 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

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