GMAT Math Sample Questions  Number Theory
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 difficulty in solving the question, 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
 Correct AnswerChoice (C).
The smallest value possible for 'a' is 363. Correct answer  Explanatory Answer
 Factors & Divisibility
 Medium
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
 Correct AnswerChoice (B).
7 such positive integers exist. Correct answer  Explanatory Answer
 Number Properties
 Easy
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
 Correct AnswerChoice (D).
The value of the divisor is 37. Correct answer  Explanatory Answer
 Divisors & Remainders
 Medium
How many keystrokes are needed to type numbers from 1 to 1000?
 3001
 2893
 2704
 2890
 None of these
 Correct AnswerChoice (B).
2893 keystrokes are required. Correct answer  Explanatory Answer
 Counting Methods
 Easy
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
 Correct AnswerChoice (C).
The value of the divisor is 13. Correct answer  Explanatory Answer
 Remainders & Divisors
 Medium
How many integral divisors does the number 120 have?
 14
 16
 12
 20
 None of these
 Correct AnswerChoice (B).
120 has 16 integral divisors. Correct answer  Explanatory Answer
 Number of Divisors
 Medium
How many trailing zeros will be there after the rightmost nonzero digit in the value of 25! (factorial 25)?
 25
 8
 6
 5
 2
 Correct AnswerChoice (C).
There are 6 trailing zeroes in 25!. Correct answer  Explanatory Answer
 Factorials
 Medium
What is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33?
 3
 27
 30
 21
 18
 Correct AnswerChoice (C).
The remainder is 30. Correct answer  Explanatory Answer
 Remainders
 Medium
Data Sufficiency : Is x^{3} > x^{2} ?
 x > 0
 x < 1
 Correct AnswerChoice (B).
Statement 2 alone is sufficient; statement 1 is not. Correct answer  Explanatory Answer
 Indices
 Medium
Data Sufficiency : Is a terminating decimal?
 x is a multiple of 2
 y is a multiple of 3
 Correct AnswerChoice (E).
The two statements together are NOT sufficient. Correct answer  Explanatory Answer
 Terminating Decimals
 Medium
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
 Correct AnswerChoice (D).
EACH statement ALONE is sufficient. Correct answer  Explanatory Answer
 Test of Divisibility
 Easy
Data Sufficiency : If x and y are positive integers, is y odd?
 x is odd.
 xy is odd.
 Correct AnswerChoice (B).
Statement 2 alone is sufficient; statement 1 is not. Correct answer  Explanatory Answer
 Odd and even integers
 Easy
Data Sufficiency : Is xy < 0?
 5x + y = 0
 x + 5y = 0
 Correct AnswerChoice (D).
EACH statement ALONE is sufficient. Correct answer  Explanatory Answer
 Absolute values
 Medium
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.
 Correct AnswerChoice (A).
Statement 1 alone is sufficient; statement 2 is not. Correct answer  Explanatory Answer
 Divisors & Remainders
 Hard
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
 Correct AnswerChoice (A).
Statement 1 alone is sufficient; statement 2 is not. Correct answer  Explanatory Answer
 Number Properties
 Medium
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