CAT Practice : Number System: Remainders

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The following topics are covered in the CAT quant section from Number system - Remainders. Detailed explanatory answers, solution videos and slide decks are also provided.

  1. 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

  2. Number Theory - Binomial Theorem

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

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

  3. 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

  4. 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

  5. Remainders - factorization properties

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

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

  6. 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       Correct answer
    • Explanatory Answer
    • Possible remainders
    • Hard

  7. 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

  8. 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

  9. 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       Correct answer
    • Explanatory Answer
    • Remainders - basics
    • Medium

  10. 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

  11. 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

  12. 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       Correct answer
    • Explanatory Answer
    • Divisibility - Large Number
    • Medium

  13. 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

  14. 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       Correct answer
    • Explanatory Answer
    • Remainder - Large number
    • Medium

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