# GMAT Hard Math Questions | Arithmetic

#### Must Solve GMAT Practice Questions | 700 800 Level Questions

Must solve GMAT practice questions in arithmetic. These GMAT hard math questions include both problem solving and data sufficiency questions. The following topics are covered in the GMAT quant section from arithmetic:

1. Number Properties & Theory
2. Ratio and Proportions
3. Percents
4. Powers and Roots of Numbers
5. Descriptive Statistics
6. Sets
7. Counting Methods: Permutation & Combination

1. #### 700 800 Level GMAT Sample Question | Probability

If two distinct integers a and b are picked from {1, 2, 3, 4, .... 100} and multiplied, what is the probability that the resulting number has EXACTLY 3 factors?

1. 23
2. 21
3. 25
4. 26
5. 24

5. #### 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

6. #### GMAT Challenging Math Question | Arithmetic | Number Properties DS Practice

Is |x| > x?

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

7. #### GMAT 700 800 Level Question | Coordinate Geometry & Permutation Combination

Rectangle ABCD is constructed in the xy-plane so that sides AB and CD are parallel to the x-axis. Both the x and y coordinates of all four vertices of the rectangle are integers. How many rectangles can be constructed if x and y coordinates satisfy the inequality 11 < x < 29 and 5 ≤ y ≤ 13?

1. 153
2. 153C4
3. 4896
4. 2448
5. 5508

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 9. #### GMAT 700 Level Sample Question in Counting Methods 149 is a 3-digit positive integer, product of whose digits is 1 × 4 × 9 = 36. How many 3-digit positive integers exist, product of whose digits is 36? 1. 21 2. 27 3. 9 4. 45 5. 12 10. #### GMAT Hard Math Arithmetic | Permutation Combination - Selections | GMAT Problem Solving A student is required to solve 6 out of the 10 questions in a test. The questions are divided into two sections of 5 questions each. In how many ways can the student select the questions to solve if not more than 4 questions can be chosen from either section? 1. 100 2. 210 3. 150 4. 200 5. 105 11. #### GMAT 700 800 Level Question | Arithmetic | Counting Methods Problem Solving How many 6-digit numbers can be formed using the digits {1, 2, 3, ... 9} such that any digit that appears in such a number appears at least twice? 1. 1809 2. 7569 3. 9369 4. 8649 5. 8289 12. #### 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 13. #### GMAT Data Sufficiency | Challenging Number Properties & Inequalities Question Is x |x| = x2? Statement 1: x$1 – x2) < 0
Statement 2: x(1 – x) < 0

14. #### GMAT DS Sample Question | Statistics | Mean Median Range

What is the range of 5 distinct single digit positive integers if their average is 5?

Statement 1: Their median is 6.
Statement 2: The average of the 3 largest among the 5 numbers is 7.

15. #### GMAT Challenging Question | Arithmetic | Numbers & Progressions DS

What is the range of 3 positive integers a, b, and c?

Statement 1: 21a = 9b = 7c
Statement 2: a + 8, b, and c, in that order are in AP.

16. #### 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.

17. #### 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

18. #### 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

19. #### 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

20. #### 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.

21. #### GMAT DS Sample Question | Arithmetic - Statistics | Mean, Median, and Range

If sets A and B have n elements each, are the ranges of the two sets equal?

Statement 1: Both sets are symmetric about their respective means.
Statement 2: The median of both the sets is 50.

22. #### 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

23. #### GMAT Arithmetic Question | Numbers Counting Methods Problem Solving

How many even 3-digit positive integers with distinct digits are there?

1. 400
2. 320
3. 328
4. 356
5. 408

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