# 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 not 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 Answer**Choice (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 Answer**Choice (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 Answer**Choice (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 Answer**Choice (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 Answer**Choice (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 Answer**Choice (B).

120 has 16 integral divisors. Correct answer- Explanatory Answer
- Number of Divisors
- Medium

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

**Correct Answer**Choice (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 Answer**Choice (C).

The remainder is 30. Correct answer- Explanatory Answer
- Remainders
- Medium

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

**Correct Answer**Choice (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 Answer**Choice (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 Answer**Choice (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 Answer**Choice (B).

Statement 2 alone is sufficient; statement 1 is not. Correct answer- Explanatory Answer
- Odd and even integers
- Easy

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

**Correct Answer**Choice (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 Answer**Choice (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 Answer**Choice (A).

Statement 1 alone is sufficient; statement 2 is not. Correct answer- Explanatory Answer
- Number Properties
- Medium

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