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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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

   A school has less than 5000 students and if the students are divided equally into teams of either 9 or 10 or 12 or 25 each, exactly 4 are always left out. However, if they are divided into teams of 11 each, no one is left out. The maximum number of teams of 12 each that can be formed out of the students in the school is

   Correct Answer150

   Video ExplanationExplanation

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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 division problem, product of quotient and the remainder is 24 while their sum is 10. If the divisor is 5 then dividend is __________.

   Correct Answer34
   

   Explanation

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2. IPMAT 2019 Question Paper - IPM Indore Quants

   The remainder when \29^{29^{29}}\\) is divided by 9 is

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

   Correct AnswerChoice B
   2

   ExplanationVideo Solution

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