CAT Questions | CAT Number Theory: Remainders Questions

A CAT Number Systems: Remainders question that appears in the Quantitative Aptitude section of the CAT Exam broadly tests an aspirant on the concepts - Remainder Theory, Successive Remainders, Test of Divisibility and so on. In CAT Exam, one can generally expect to get approx. 1 question from CAT Number Systems: Remainders. 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 Theory: Remainders - Sum of Digits

   The sum of the digits of a number N is 23. The remainder when N is divided by 11 is 7. What is the remainder when N is divided by 33?

   1. 7
   2. 29
   3. 16
   4. 13

   Correct AnswerChoice B
   29

   Explanation Video Solution

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2. CAT Number Theory - Binomial Theorem

   What is the remainder when (13¹⁰⁰ + 17¹⁰⁰) is divided by 25?

   1. 0
   2. 2
   3. 4
   4. 11

   Correct AnswerChoice B
   2

   Explanation

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3. CAT Number Theory Remainders

   A number when divided by 18 leaves a remainder 7. The same number when divided by 12 leaves a remainder n. How many values can n take?

   1. 2
   2. 0
   3. 1
   4. 3

   Correct AnswerChoice A
   2

   Explanation

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4. CAT Remainders

   N leaves a remainder of 4 when divided by 33, what are the possible remainders when N is divided by 55?

   1. 3
   2. 5
   3. 4
   4. 2

   Correct AnswerChoice B
   5

   Explanation

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5. CAT Remainders - Factorization Properties

   What is the remainder when we divide 3⁹⁰ + 5⁹⁰ by 34?

   1. 0
   2. 17
   3. 33
   4. 1

   Correct AnswerChoice A
   0

   Explanation

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6. CAT Remainders - Squares

   N² leaves a remainder of 1 when divided by 24. What are the possible remainders we can get if we divide N by 12?

   1. 1, 5, 7 and 11
   2. 1 and 5
   3. 5, 9, and 11
   4. 1 and 11

   Correct AnswerChoice A
   1, 5, 7 and 11

   Explanation

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7. CAT Remainders, coprime numbers

   A prime number p greater than 100 leaves a remainder q on division by 28. How many values can q take?

   1. 8
   2. 12
   3. 9
   4. 15

   Correct AnswerChoice B
   12

   Explanation

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8. CAT Remainders and LCM

   How many positive integers are there from 0 to 1000 that leave a remainder of 3 on division by 7 and a remainder of 2 on division by 4?

   1. 32
   2. 36
   3. 24
   4. 19

   Correct AnswerChoice B
   36

   Explanation

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9. CAT Remainders - Basics

   Three numbers leave remainders of 43, 47 and 49 on division by N. The sum of the three numbers leaves a remainder 9 on division by N. What are the values N can take?

   1. 65
   2. 96
   3. 125
   4. More than one value is possible

   Correct AnswerChoice D
   More than one value is possible

   Explanation

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10. CAT Remainders

    A number leaves a remainder 3 on division by 14, and leaves a remainder k on division by 35. How many possible values can k take?

    1. 3
    2. 2
    3. 5
    4. 4

    Correct AnswerChoice C
    5

    Explanation

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11. CAT Number Systems: Remainders - Large number

    Consider a large number N = 1234567891011121314………979899100. What is the remainder when first 100 digits of N is divided by 9?

    1. 0
    2. 8
    3. 1
    4. 5

    Correct AnswerChoice D
    5

    Explanation

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12. CAT Number Systems - Divisibility - Large Number

    Given a number, N = 55⁵ + 17⁵ – 72⁵, then which of the following is true?

    1. N is divisible by both 7 and 13
    2. N is divisible by both 3 and 17
    3. N is divisible by 17 but not 3
    4. N is divisible by 11 but not 17

    Correct AnswerChoice B
    N is divisible by both 3 and 17

    Explanation

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13. CAT Number Systems - Same remainder

    The integers 573921 and 575713 when divided by a 3 digit number leave the same remainder. What is that 3 digit number?

    1. 206
    2. 256
    3. 274
    4. 189

    Correct AnswerChoice B
    256

    Explanation

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14. CAT Remainder - Large number

    If N = (24³ + 25³ + 26³ + 27³), then N divided by 102 leaves a remainder of?

    1. 18
    2. 12
    3. 1
    4. 0

    Correct AnswerChoice D
    0

    Explanation

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