GMAT Maths | Number Properties & AP GP

GMAT Sample Questions | Number Theory, Sequence & Series Questionbank Page 1

You should expect to get five to seven questions from number systems, number properties and number theory and one or two questions from sequence and series (arithmetic sequence and geometric sequence) in the GMAT quant section - in both variants viz., problem solving and data sufficiency. In number properties, concepts tested include multiples, factors, LCM, HCF, perfect squares, prime factorization, number of factors, remainders, factorials, and odd - even numbers. In sequence and series, arithmetic progression and geometric progression is tested. In addition, questions could define a sequence that is neither an arithmetic sequence nor a geometric sequence.

If you have difficulty in solving these GMAT sample questions in number properties and progressions, go to the explanatory answer or the video explanations (wherever provided) to learn how to solve these GMAT practice questions.

If it has been a while since you did maths, you should start by watching these two GMAT Math lesson videos to help you get better traction when solving the questions given below.


  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
    Choice C
    363 is the smallest value.
    Hint to solve this GMAT number properties sample question

    This GMAT question is a number properties question - concept tested is factors. If 112 and 33 are factors of the number, the number should contain 112 and 33. Excluding 'a' prime factorize the remaining part of the given number. Identify what prime factors are missing in the prime factorised part of the number. The missing component should be a part of 'a' so that the number is divisible by 112 and 33. A 650 to 700 level GMAT sample question in number properties & number theory.


  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
    Choice B
    7 Positive integers
    Hint to solve this GMAT counting methods question

    This GMAT question is a number properties counting methods question. You can approach it in two ways. I will outline the first one in the hint. Find the answer and check the explanatory answer for the alternative method. Find the number of single digit, two-digit, and three-digit numbers that meet the criterion. Extrapolate to find the final answer. A GMAT 650 to 700 level math problem solving question.


  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
    Choice D
    K = 9
    Hint to solve this division algorithm question

    This GMAT sample question is a number properties problem solving question. Express the first division in the standard framework - i.e., using Euclid's division algorithm.

    Let the number be 'n', the divisor be 'd' and the quotient of the division be 'q'. So, n = qd + 24. Repeat the process when twice the number is divided by 'd'. Use the property that the remainder of the division should be lesser than the divisor to compute the divisor. A 700 level GMAT practice question.



  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
    Choice B
    2893 Keystrokes
    Approach to solve this GMAT number systems and counting methods question

    This GMAT sample question is an elementary counting methods question. The best way to solve this question is to compute keystrokes required to type single digit, two-digit, three-digit numbers and 1000. Watch out when you compute the number of 2-digit and 3-digit numbers. That is the only trap in this question. A 600 level GMAT math question combining numbers systems and counting methods.


  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. However, 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
    Choice C
    13 is the divisor
    Hint to solve GMAT Number Properties Question

    This GMAT question tests remainder concepts and is a problem solving question in number properties. Knowing the two rules mentioned below will help you solve this GMAT practice question.

    Rule 1: The remainder of the sum of two more numbers is equal to the sum of the remainders of those numbers.
    Rule 2: The remainder of dividing a number by a divisor 'd' will be lesser than the divisor.

    A 650 to 700 level GMAT practice question in number properties.


  6. How many integral divisors does the number 120 have?

    1. 14
    2. 16
    3. 12
    4. 20
    5. None of these
    Choice B
    16 Integral factors
    Approach to solve this GMAT factors question

    This GMAT practice question is a number properties problem solving question in factors.

    Step 1: Prime factorise the given number.
    Step 2: The number of factors of the number = product of the powers of the prime factors of the number after incrementing each power by 1.

    A 650 to 700 level GMAT sample question in the GMAT Math section.


  7. How many trailing zeros will be there after the rightmost non-zero digit in the value of 25!?

    1. 25
    2. 8
    3. 6
    4. 5
    5. 2
    Choice C
    6 Trailing zeros
    Approach to solve this number properties question in factorials

    This GMAT sample question is a medium difficulty problem solving question in number properties. The number of trailing zeroes in the decimal representation of 25! is the highest power of 10 that will divide 25! without leaving any remainder. The highest power of 10 that will divide 25! is the same as the highest power of 5 that will divide 25!

    Successive division of 25 by 5 and adding the quotients of the division will yield the required answer.

    A 700 level GMAT question in number properties.


  8. What is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33?

    1. 3
    2. 27
    3. 30
    4. 21
    5. 18
    Choice C
    The remainder is 30.
    Hint to solve this GMAT number theory question

    This GMAT question is a problem solving question in number theory. Applying the following 2 rules about division will help you get the answer.

    Rule 1: The remainder of the product of two or more numbers is the same sa the product of the remainders of those numbers.
    Rule 2: The remainder of dividing a number by a divisor 'd' is less than the divisor 'd'.

    A 650 to 700 level GMAT question in remainders.


  9. Data Sufficiency: Is x3 > x2?

    1. x > 0
    2. x < 1
    Choice B
    Approach to solve this GMAT number properties Data Sufficiency problem

    This GMAT sample question is a number properties DS question. The data is sufficient if we can answer the question with a definite yes or definite no.

    When evaluating different powers of 'x', the break points are -1, 0, and 1. So, as a standard approach, check what the answer is when x < -1, -1 < x < 0, 0 < x < 1, x > 1 if you see a question that compares two different powers of an unknown. Also evaluate the answer at the break points - i.e., when x = -1, x = 0 and x = 1. A 650 to 700 level GMAT data sufficiency question.


  10. Data Sufficiency: Is \\frac{x}{y}\\) a terminating decimal?

    1. x is a multiple of 2
    2. y is a multiple of 3
    Choice E
    Hint to solve this GMAT number systems DS question

    This GMAT question is a number systems data sufficiency question. A value of a fraction will be a terminating decimal if the denominator contains a prime factor other than 2 or 5.

    Look for a counter example for each of the statements. If you are able to find a counter example, the data is not sufficient. A 650 to 700 level GMAT sample question in number systems.


  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
    Choice D
    Hint to solve this GMAT Number Systems Question

    This GMAT practice question is a data sufficiency practice question in tests of divisibility in number systems. The test of divisibility by 21 is that the number should be divisible by both 3 and 7. If it fails for either one, the number is not divisible by 21. With the information in the two statements whether you are able to determine this information. A 650 to 700 level GMAT sample question in number systems.


  12. Data Sufficiency: If x and y are positive integers, is y odd?

    1. x is odd.
    2. xy is odd.
    Choice B
    Hint to solve this GMAT DS question in number systems

    This GMAT sample question is a number systems DS question. The product of two integers is odd only when both the numbers are odd. Use this property to evaluate whether 'y' is odd. A sub 600 level GMAT practice question in data sufficiency.


  13. Data Sufficiency: Is xy < 0?

    1. 5|x| + |y| = 0
    2. |x| + 5|y| = 0
    Choice D
    Hint to solve this GMAT absolute values DS question

    This GMAT practice question is an algebra and number properties data sufficiency question. |x| or |y| cannot be negative. So, if the sum of the absolute values of two numbers is 0, it is possible only when both the numbers are 0. A 600 level GMAT question in absolute values and number systems.


  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.
    Choice A
    Hint to solve this GMAT Number Properties DS question

    This GMAT sample question is a number properties DS question testing concepts in remainders. Use the following rules about remainders to solve the DS question.

    Rule 1: Remainder of the sum of two numbers is the same as the sum of the remainders of the two numbers.
    Rule 2: Remainder obtained when dividing a number by a divisor 'd' is lesser than the divisor.

    Using the information given in the two statements, evaluate whether you could find a unique value for the divisor.

    A 700 level GMAT data sufficiency question in number properties.


  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
    Choice A
    Hint to solve this Number Systems Data Sufficiency question

    The key data is that each of x, y, and z is less than 10. Use this information along with the data given in the statements to determine how many of these 3 numbers are positive. A 600 to 650 level GMAT question in number systems.


 

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