You may get five to seven questions from Number systems, number properties and number theory and one or two questions from sequences and series 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, and arithmetic and geometric progressions.

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

If both 11

^{2}and 3^{3}are factors of the number a * 4^{3}* 6^{2}* 13^{11}, then what is the smallest possible value of a?- 121
- 3267
- 363
- 33
- None of the above

How many different positive integers exist between 10

^{6}and 10^{7}, the sum of whose digits is equal to 2?- 6
- 7
- 5
- 8
- 18

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?

- 13
- 59
- 35
- 37
- 12

How many keystrokes are needed to type numbers from 1 to 1000??

- 3001
- 2893
- 2704
- 2890
- None of these

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?

- 11
- 17
- 13
- 23
- None of these

How many integral divisors does the number 120 have?

- 14
- 16
- 12
- 20
- None of these

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

- 25
- 8
- 6
- 5
- 2

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

- 3
- 27
- 30
- 21
- 18

__Data Sufficiency__: Is x^{3}> x^{2}?- x > 0
- x < 1

__Data Sufficiency__: Is a terminating decimal?- x is a multiple of 2
- y is a multiple of 3

__Data Sufficiency__: Is the positive integer X divisible by 21?- When X is divided by 14, the remainder is 4
- When X is divided by 15, the remainder is 5

__Data Sufficiency__: If x and y are positive integers, is y odd?- x is odd.
- xy is odd.

__Data Sufficiency__: Is xy < 0?- 5|x| + |y| = 0
- |x| + 5|y| = 0

__Data Sufficiency__: When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?- When 2x is divided by d, the remainder is 23.
- When 3x is divided by d, the remainder is 22.

__Data Sufficiency__: How many of the numbers x, y, and z are positive if each of these numbers is less than 10?- x + y + z = 20
- x + y = 14

What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?

- 897
- 164,850
- 164,749
- 149,700
- 156,720

How many 3 digit positive integers exist that when divided by 7 leave a remainder of 5?

- 128
- 142
- 143
- 141
- 129

The average of 5 consecutive integers starting with m as the first integer is n. What is the average of 9 consecutive integers that start with (m + 2)?

- m + 4
- n + 6
- n + 3
- m + 5
- n + 4

The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 15 terms of the arithmetic progression?

- 300
- 120
- 150
- 170
- 270

If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 9, what is the common ratio of the G.P?

- 3
- \\frac {1} {3})
- 2
- 9
- \\frac {1} {9})

Set A contains all the even numbers between 2 and 50

__inclusive__. Set B contains all the even numbers between 102 and 150__inclusive__. What is the difference between the sum of elements of set B and the sum of the elements of set A?- 2500
- 5050
- 11325
- 6275
- 2550

__Data Sufficiency__: A set S contains the following elements: {7, 11, 15, 19, 23, x}. What is the value of x?- The elements are in arithmetic progression.
- x is prime.

In the first 1000 natural numbers, how many integers exist such that they leave a remainder 4 when divided by 7, and a remainder 9 when divided by 11?

- 11
- 14
- 12
- 13
- 10

__Data Sufficiency__: What is the 6^{th}term of the Arithmetic sequence?- The sum of the 6
^{th}to the 12^{th}term of the sequence is 77. - The sum of the 2
^{nd}to the 10^{th}term of the sequence is 108.

- The sum of the 6
__Data Sufficiency__: What is the value of X, if X and Y are two distinct integers and their product is 30?- X is an odd integer.
- X > Y.

__Data Sufficiency__: Is y an integer?- y
^{3}is an integer - 3y is an integer

- y
__Data Sufficiency__: Is the positive integer m divisible by 6?- m is divisible by 3
- m is divisible by 4

__Data Sufficiency__: Is ab positive?- (a + b)
^{2}< (a - b)^{2} - a = b

- (a + b)
__Data Sufficiency__: When Y is divided by 2, is the remainder 1?- (-1)
^{(Y+2)}= -1 - Y is prime.

- (-1)
__Data Sufficiency__: Is the two digit positive integer P a prime number?- (P + 2) and (P - 2) are prime.
- (P - 4) and (P + 4) are prime.

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