CAT Practice : Number System

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

    How many numbers with distinct digits are possible product of whose digits is 28?

    1. 6
    2. 4
    3. 8
    4. 12
  2. Sum of first n natural numbers

    A page is torn from a novel. The sum of the remaining digits is 10000. What is the sum of the two page-numbers on the torn page of this novel?

    1. 77 and 78
    2. 33 and 34
    3. 8 and 9
    4. None of these
  3. Perfect Square

    A 4-digit number of the form aabb is a perfect square. What is the value of a - b?

    1. 3
    2. 2
    3. 4
    4. 1
  4. Last two digits

    What are the last two digits of the number 745?

    1. 07
    2. 23
    3. 49
    4. 43
  5. Multiples

    n2 + 5n + 6 is a multiple of 6. n is natural number less than 100. How many values can n take?

    1. 33
    2. 65
    3. 66
    4. 67
  6. Greatest integer function

    [x] is the greatest integer less than or equal to x. Find the number of positive integers n such that .

    1. 31
    2. 25
    3. 35
    4. 40
    • Correct AnswerChoice (C).
      35
      Correct answer
    • Explanatory Answer
    • Greatest integer function
    • Medium
  7. Medians, Number

    Positive numbers 1 to 55, inclusive are placed in 5 groups of 11 numbers each. What is the maximum possible average of the medians of the 5 groups?

    1. 34
    2. 28
    3. 35
    4. 38
  8. 44th digit of a number

    N is an 80-digit positive integer (in the decimal scale). All digits except the 44th digit (from the left) are 2. If N is divisible by 13, find the 26th digit?

    1. 5
    2. 6
    3. 1
    4. 2

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