CAT Questions | CAT Number Theory: Remainders Questions

CAT Quantitative Aptitude | CAT Number Theory Remainders

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
    Choice B
    29

  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
    Choice B
    2

  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
    Choice A
    2

  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
    Choice B
    5

  5. CAT Remainders - Factorization Properties

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

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

  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
    Choice A
    1, 5, 7 and 11

  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
    Choice B
    12

  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
    Choice B
    36

  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
    Choice D
    More than one value is possible

  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
    Choice C
    5

  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
    Choice D
    5

  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
    Choice B
    N is divisible by both 3 and 17

  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
    Choice B
    256

  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
    Choice D
    0

  15. The following questions are from IPMAT Rohtak and Indore sample papers. If you want to take these questions as a mock please click below.

    IPMAT Rohtak Sample Paper Mock
    IPMAT Indore Sample Paper Mock

    Please note that the explanation button will take you to the IPMAT solution page.


  16. IPMAT 2019 Question Paper - IPM Indore Quants,Remainders

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

    1. 1
    2. 2
    3. 3
    4. 4
    Choice B
    2


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