1. Question 13 of the Must Solve 100 GMAT quant question series by q-51.com.

This question is a descriptive statistics question and tests concepts in mean and median of 3 numbers.

Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a +11), what is the least possible value of c?
A. 23
B. 21
C. 25
D. 26
E. 24

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2. Concept covered in this question is absolute value. How to work around algebraic expressions with absolute value?

If x and y are integers and |x - y| = 12, what is the minimum possible value of xy?
A. -12
B. -18
C. -24
D. -36
E. -48

Visit gmatpractice.q-51.com for tough GMAT quant questions. Collection of must solve 100 gmat quant questions by 4GMAT.

3. This question tests concepts in mean, median and range and also includes elementary number properties such as prime numbers and odd and even numbers.

Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and y are both prime numbers and 0 < x < 40 and 0 < y < 40, which of the following MUST be true?

I. The maximum possible range of the set is greater than 33.
II. The median can never be an even number.
III. If y = 37, the average of the set will be greater than the median.

A. I only
B.I and II only
C. I and III only
D. III only
E. I, II, and III

Part of the Q-51 series by 4GMAT. Visit gmatpractice.q-51.com for more practice questions

4. Part of the Q-51 series by 4GMAT, this question is a problem solving question and tests concepts in absolute values. An algebra topic.

If a, b, and c are not equal to zero, what is the difference between the maximum and minimum value of S?
S = 1 + {|a|/a} + 2{|b|/b} + 3{|ab|/ab} - 4{|c|/c}
A. 12
B. 14
C. 22
D. 20
E. 18

Solution and video explanation to this GMAT hard math question provided by 4GMAT. Visit gmatpractice.q-51.com for more questions

5. This tough GMAT quant question is a problem solving question in geometry. The question is to find the area of a shape which is a portion of two equal semicircles. The concept tested are one's ability to segregate the semicircle into parts for which area can be found. This question is a part of the q-51.com series by 4GMAT.

In the figure given below, ABC and CDE are two identical semi-circles of radius 2 units. B and D are the mid points of the arc ABC and CDE respectively. What is the area of the shaded region?
A. 4π - 1
B. 3π - 1
C. 2π - 4
D. (3π−1)/2
E. 2π - 2

Detailed video explanation to this hard math GMAT question is provided in this video. Presented by K S Baskar of 4GMAT.
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# Q51 GMAT Hard Math Questions

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