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GMAT Math Sample Questions - Number Theory

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You may get three to five questions from Number systems, number properties and number theory in the GMAT quant section - in both variants viz., problem solving and data sufficiency. The concepts tested include LCM, HCF, perfect squares, prime factorization, number of factors, remainders, factorials, odd and even numbers. A collection of GMAT practice questions in number system and number properties is given below. Attempt these questions and check whether you have got the correct answer. If you have not go to the explanatory answer or the video explanations (wherever provided) to learn how to crack the question.

  1. If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of a?

    1. 121
    2. 3267
    3. 363
    4. 33
    5. None of the above
    • Correct AnswerChoice (C).
      The smallest value possible for 'a' is 363.
      Correct answer
    • Explanatory Answer
    • Factors & Divisibility
    • Medium
  2. How many different positive integers exist between 106 and 107, the sum of whose digits is equal to 2?

    1. 6
    2. 7
    3. 5
    4. 8
    5. 18
    • Correct AnswerChoice (B).
      7 such positive integers exist.
      Correct answer
    • Explanatory Answer
    • Number Properties
    • Easy
  3. A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?

    1. 13
    2. 59
    3. 35
    4. 37
    5. 12
    • Correct AnswerChoice (D).
      The value of the divisor is 37.
      Correct answer
    • Explanatory Answer
    • Divisors & Remainders
    • Medium
  4. How many keystrokes are needed to type numbers from 1 to 1000?

    1. 3001
    2. 2893
    3. 2704
    4. 2890
    5. None of these
    • Correct AnswerChoice (B).
      2893 keystrokes are required.
      Correct answer
    • Explanatory Answer
    • Counting Methods
    • Easy
  5. When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9. When the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4. What is the value of the divisor?

    1. 11
    2. 17
    3. 13
    4. 23
    5. None of these
    • Correct AnswerChoice (C).
      The value of the divisor is 13.
      Correct answer
    • Explanatory Answer
    • Remainders & Divisors
    • Medium
  6. How many integral divisors does the number 120 have?

    1. 14
    2. 16
    3. 12
    4. 20
    5. None of these
    • Correct AnswerChoice (B).
      120 has 16 integral divisors.
      Correct answer
    • Explanatory Answer
    • Number of Divisors
    • Medium
  7. How many trailing zeros will be there after the rightmost non-zero digit in the value of 25! (factorial 25)?

    1. 25
    2. 8
    3. 6
    4. 5
    5. 2
    • Correct AnswerChoice (C).
      There are 6 trailing zeroes in 25!.
      Correct answer
    • Explanatory Answer
    • Factorials
    • Medium
  8. What is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33?

    1. 3
    2. 27
    3. 30
    4. 21
    5. 18
    • Correct AnswerChoice (C).
      The remainder is 30.
      Correct answer
    • Explanatory Answer
    • Remainders
    • Medium
  9. Data Sufficiency : Is x3 > x2 ?

    1. x > 0
    2. x < 1
    • Correct AnswerChoice (B).
      Statement 2 alone is sufficient; statement 1 is not.
      Correct answer
    • Explanatory Answer
    • Indices
    • Medium
  10. Data Sufficiency : Is x/y a terminating decimal?

    1. x is a multiple of 2
    2. y is a multiple of 3
    • Correct AnswerChoice (E).
      The two statements together are NOT sufficient.
      Correct answer
    • Explanatory Answer
    • Terminating Decimals
    • Medium
  11. Data Sufficiency : Is the positive integer X divisible by 21?

    1. When X is divided by 14, the remainder is 4
    2. When X is divided by 15, the remainder is 5
    • Correct AnswerChoice (D).
      EACH statement ALONE is sufficient.
      Correct answer
    • Explanatory Answer
    • Test of Divisibility
    • Easy
  12. Data Sufficiency : If x and y are positive integers, is y odd?

    1. x is odd.
    2. xy is odd.
    • Correct AnswerChoice (B).
      Statement 2 alone is sufficient; statement 1 is not.
      Correct answer
    • Explanatory Answer
    • Odd and even integers
    • Easy
  13. Data Sufficiency : Is xy < 0?

    1. 5|x| + |y| = 0
    2. |x| + 5|y| = 0
    • Correct AnswerChoice (D).
      EACH statement ALONE is sufficient.
      Correct answer
    • Explanatory Answer
    • Absolute values
    • Medium
  14. Data Sufficiency : When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?

    1. When 2x is divided by d, the remainder is 23.
    2. When 3x is divided by d, the remainder is 22.
    • Correct AnswerChoice (A).
      Statement 1 alone is sufficient; statement 2 is not.
      Correct answer
    • Explanatory Answer
    • Divisors & Remainders
    • Hard
  15. Data Sufficiency : How many of the numbers x, y, and z are positive if each of these numbers is less than 10?

    1. x + y + z = 20
    2. x + y = 14
    • Correct AnswerChoice (A).
      Statement 1 alone is sufficient; statement 2 is not.
      Correct answer
    • Explanatory Answer
    • Number Properties
    • Medium
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