CAT Practice : Number System: Remainders

You are here: Home  CAT Questionbank   CAT Quant  Number System: Remainders
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

Our Online Course, Now on Google Playstore!

2IIM's App

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.


Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Get it on Google Play