CAT Questions | CAT Number Systems Questions

CAT Quantitative Aptitude | CAT Number Systems: Digits problems

A CAT Number theory question from Number Systems: Digits that appears in the Quantitative Aptitude section of the CAT Exam will consist of concepts from Digits, Test of Divisibility, Perfect squares and so on. In CAT Exam, one can expect to get 1~2 questions from CAT Number Systems: Digits. 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: 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
    Choice C
    8

  2. CAT Number Theory: Sum of first n natural numbers

    A page is torn from a novel. The sum of the remaining page numbers 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
    Choice D
    None of these

  3. CAT Number Theory: 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
    Choice A
    3

  4. CAT Number Theory: Last two digits

    What are the last two digits of the number 745?

    1. 07
    2. 23
    3. 49
    4. 43
    Choice A
    07

  5. CAT Number Theory: 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
    Choice C
    66

  6. CAT Number Theory: Greatest integer function

    [x] is the greatest integer less than or equal to x. Find the number of positive integers n such that [\\frac{n}{11}\\)] = [\\frac{n}{13}\\)] .

    1. 31
    2. 25
    3. 35
    4. 40
    Choice C
    35

  7. CAT Number Theory: 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
    Choice D
    38

  8. CAT Number Theory: 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 44th digit?

    1. 5
    2. 6
    3. 1
    4. 2
    Choice B
    6

  9. CAT Number Theory: Divisibility of powers

    A number 416 + 1 is divisible by x. Which among the following is also divisible by x?

    1. 496 + 1
    2. 432 + 1
    3. 48 + 1
    4. 448 + 1
    Choice D
    448 + 1

  10. CAT Number Theory: Test of Divisibility

    Which among the following is the smallest 7 digit number that is exactly divisible by 43?

    1. 1000043
    2. 1000008
    3. 1000006
    4. 1000002
    Choice B
    1000008

  11. CAT Number Theory: Three digit number combinations

    How many 3-digit positive integers, with digits a, b and c exist such that a < b and c < b? Assume that a is in hundred's place, b is in ten's place, c is in unit's place and a is a non-zero digit.

    1. 450
    2. 240
    3. 364
    4. 648
    Choice B
    240

  12. 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.


  13. IPMAT 2020 Sample Paper - IPM Rohtak Quants,Number Theory

    If * = +, / = -, + = *, - = / then 43 * 561 + 500 - 100 / 10 = ?

    1. 3211
    2. 2388
    3. 2883
    4. 2838
    Choice D
    2838

  14. IPMAT 2019 Question Paper - IPM Indore Quants,Number Theory

    Assume that all positive integers are written down consecutively from left to right as in 1234567891011...... The 6389th digit in this sequence is

    4

  15. IPMAT 2019 Question Paper - IPM Indore Quants,Number Theory

    The number of pairs of integers whose sums are equal to their products is

    2

  16. IPMAT 2019 Question Paper - IPM Indore Quants,Number Theory

    How many different numbers can be formed by using only the digits 1 and 3 which are smaller than 3000000 ?

    1. 64
    2. 128
    3. 190
    4. 254
    Choice C
    190

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 2017 Question Paper Slot 2 - Number Theory

    The numbers 1, 2,..., 9 are arranged in a 3 X 3 square grid in such a way that each number occurs once and the entries along each column, each row, and each of the two diagonals add up to the same value. If the top left and the top right entries of the grid are 6 and 2, respectively, then the bottom middle entry is: [TITA]

    3

  2. CAT 2017 Question Paper Slot 2 - Number Theory

    If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is

    1. 1777
    2. 1785
    3. 1875
    4. 1877
    Choice D
    1877

  3. CAT 2017 Question Paper Slot 2 - Number Theory

    How many different pairs (a, b) of positive integers are there such that a ≤ b and \\frac{1}{a}) + \\frac{1}{b}) = \\frac{1}{9}) ? [TITA]

    3

  4. CAT 2018 Question Paper Slot 1 - Number Theory

    While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is: [TITA]

    40

  5. CAT 2018 Question Paper Slot 1 - Number theory

    How many numbers with two or more digits can be formed with the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 so that in every such number, each digit is used at most once and the digits appear in the ascending order?[TITA]

    502

  6. CAT 2018 Question Paper Slot 2 - Number Theory

    If the sum of squares of two numbers is 97, then which one of the following cannot be their product?

    1. 64
    2. -32
    3. 16
    4. 48
    Choice A
    64

  7. CAT 2018 Question Paper Slot 2 - Number Theory

    How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits?

    1. 5
    2. 8
    3. 7
    4. 6
    Choice D
    6

  8. CAT 2019 Question Paper Slot 1 - Number theory

    The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157 : 3, then the sum of the two numbers is

    1. 50
    2. 85
    3. 95
    4. 58
    Choice A
    50

  9. CAT 2019 Question Paper Slot 2 - Number theory

    Let a, b, x, y be real numbers such that a2 + b2 = 25 , x2 + y2 = 169 and ax + by = 65. If k = ay - bx, then

    1. k = 0
    2. k > \\frac{5}{13})
    3. k = \\frac{5}{13})
    4. 0 < k ≤ \\frac{5}{13})
    Choice A
    k = 0

  10. CAT 2019 Question Paper Slot 2 - Number theory

    How many pairs (m,n) of positive integers satisfy the equation the equation m2 + 105 = n2? [TITA]

    4

  11. CAT 2019 Question Paper Slot 2 - Number theory

    In a six-digit number, the sixth, that is, the rightmost, digit is the sum of the first three digits, the fifth digit is the sum of first two digits, the third digit is equal to the first digit, the second digit is twice the first digit and the fourth digit is the sum of fifth and sixth digits. Then, the largest possible value of the fourth digit is [TITA]

    7

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