GMAT Hard Math Questions | Number Properties

Must solve GMAT practice questions in Number Theory and Number Properties. A good number of questions in the GMAT quant section appear from this topic. It is a core topic. Includes concepts such as LCM, HCF, Factors, number of factors, reminders, divisors, factorial, prime numbers, composite numbers, relatively prime numbers. Focus on understanding the basics and principles behind each of the concepts. In short, it is not just sufficient to know how to find the LCM of two or more numbers - you also need to know what LCM actually means and in what scenario will one find the LCM of numbers.

1. GMAT Hard Math Data Sufficiency Question

   Is x³ > x²?

   Statement 1: x > 0
   Statement 2: x < 1

   Correct AnswerChoice B
   Statement (2) alone is sufficient

   Solution Video Solution

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2. GMAT Hard Math Question | Number Properties DS Practice

   What is the remainder when the positive integer x is divided by 6?

   Statement 1: When x is divided by 7, the remainder is 5.
   Statement 2: When x is divided by 9, the remainder is 3.

   Correct AnswerChoice E
   Statements Together NOT Sufficient

   Solution Video Solution

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3. GMAT Hard Math Algebra - Absolute Values | GMAT Problem Solving

   If x and y are integers and |x - y| = 12, what is the minimum possible value of xy?

   1. -12
   2. -18
   3. -24
   4. -36
   5. -48

   Correct AnswerChoice D
   The minimum possible value for xy is -36.

   Solution Video Solution

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4. GMAT Hard Math | Arithmetic | Permutation Combination Sample Question

   How many four-digit positive integers exist that contain the block 25 and are divisible by 75. (2250 and 2025 are two such numbers)?

   1. 90
   2. 63
   3. 34
   4. 87
   5. 62

   Correct AnswerChoice C
   34 such four-digit numbers exist.

   Solution Video Solution

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5. GMAT Challenging Math Question | Arithmetic | Number Properties DS Practice

   Is |x| > x?

   Statement 1: x² + y² = 4
   Statement 2: x³ + y² = 0

   Correct AnswerChoice C
   Statements Together are Sufficient.

   Solution Video Solution

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6. GMAT Hard Math Question | Algebra & Numbers | Difficult Equations Question

   Susan invited 13 of her friends for her birthday party and created return gift hampers comprising one each of $3, $4, and $5 gift certificates. One of her friends did not turn up and Susan decided to rework her gift hampers such that each of the 12 friends who turned up got $13 worth gift certificates. How many gift hampers did not contain $5 gift certificates in the new configuration?

   1. 5
   2. 2
   3. 9
   4. 3
   5. 7

   Correct AnswerChoice D
   3 gift hampers did not have $5 certificates.

   Solution Video Solution

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7. GMAT Hard Math Questions | Arithmetic | Number Properties DS

   x is a two-digit positive integer. y is obtained by multiplying the tens place of x by 2. Is y > \\frac{x}{6})?

   Statement 1: 20 < x < 30
   Statement 2: y = 10

   Correct AnswerChoice B
   Statement 2 ALONE is sufficient.

   Solution Video Solution

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8. GMAT Hard Math | Arithmetic | Number Properties Sample Question

   If y is the highest power of a number 'x' that can divide 101! without leaving a remainder, then for which among the following values of x will y be the highest?

   1. 111
   2. 462
   3. 74
   4. 33
   5. 210

   Correct AnswerChoice E
   When x = 210.

   Solution Video Solution

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9. GMAT Data Sufficiency | Challenging Number Properties & Inequalities Question

   Is x |x| = x²?

   Statement 1: x(1 – x²) < 0
   Statement 2: x(1 – x) < 0

   Correct AnswerChoice E
   Statements NOT sufficient.

   Solution Video Solution

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10. GMAT Hard Math Questions | Arithmetic | Number Properties DS

    Is the twelve-digit positive integer a perfect square?

    Statement 1: The number comprises only the digits 0, 1, and 2, each written four times.
    Statement 2: The sum of the digits of the twelve-digit number is 12.

    Correct AnswerChoice D
    Statements INDEPENDENTLY sufficient.

    Solution Video Solution

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11. GMAT 650 Level Sample Question | Arithmetic DS | Number Properties

    If a and b are positive integers, is (a + b) prime?

    Statement 1: 13a = 43b
    Statement 2: 8a = 15b

    Correct AnswerChoice A
    Statement 1 ALONE sufficient.

    Solution Video Solution

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12. GMAT Hard Math Arithmetic - Counting Methods | GMAT Problem Solving

    What is the sum of all 3-digit positive integers such that all the digits of each of the number is even?

    1. 55,500
    2. 1300
    3. 44,400
    4. 247,275
    5. 54,400

    Correct AnswerChoice E
    54,400

    Solution Video Solution

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13. GMAT Challenging Math Question | Arithmetic | Number Properties - Remainders

    What is the least number that when divided by 44 leaves a remainder 31, when divided by 56 leaves a remainder 43, and when divided by 32 leaves a remainder 19?

    1. 2464
    2. 2477
    3. 2451
    4. 616
    5. 603

    Correct AnswerChoice C
    2451

    Solution Video Solution

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14. GMAT Data Sufficiency | Number Properties

    What is the value of (m + n) if m and n are positive integers?

    Statement 1: m² – n² = 105
    Statement 2: Neither m nor n is divisible by 8.

    Correct AnswerChoice E
    Data Insufficient.

    Solution Video Solution

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15. GMAT Number Properties Practice | 650 Level Question | Factors Problem Solving

    What is the product of all the factors of the cube of a positive integer 'n' if the product of all the factors of square of n is n³?

    1. n⁴
    2. n⁶
    3. n⁹
    4. n⁵
    5. Cannot be determined

    Correct AnswerChoice B
    n⁶

    Solution Video Solution

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16. GMAT Algebra Practice Question | Equations & Numbers PS

    If x and y are non-negative integers such that 4x + 7y = 68, how many values are possible for (x + y)?

    1. 11
    2. 3
    3. 5
    4. 17
    5. 14

    Correct AnswerChoice B
    3 Values.

    Solution Video Solution