# GMAT Hard Math Questions | Series 21 to 30

1. #### 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

2. #### 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

3. #### 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

4. #### 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

5. #### Geometry | Coordinate Geometry DS Practice | GMAT Challenging Math Question

Does the line L whose equation is y = mx + c cut the x-axis in the positive direction of x-axis?

Statement 1: The intercepts of Line K, perpendicular to L, are of the opposite signs.
Statement 2: Line L passes through the 4th quadrant.

6. #### GMAT Data Sufficiency | Challenging Number Properties & Inequalities Question

Is x |x| = x2?

Statement 1: x(1 – x2) < 0
Statement 2: x(1 – x) < 0

7. #### 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.

8. #### 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.

9. #### GMAT 650 Level Algebra Question | Polynomials

If a, b, .. , j are real numbers such that (a - 1)2 + (b - 2)4 + (c - 3)6 + ... + (j - 10)20 = 0, what is the value of b × d × f × h × j?

1. 120
2. 36,28,800
3. 3840
4. 240
5. 1536

10. #### 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.

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