The Average (Arithmetic Mean) of Four Distinct Positive Integers is 10 GMAT Problem Solving

Question: The average (arithmetic mean) of four distinct positive integers is 10. If the average of the smaller two of these four integers is 8, which of the following represents the maximum possible value of the largest integer?

1. 12
2. 14
3. 15
4. 16
5. 17

“The average (arithmetic mean) of four distinct positive integers is 10. If the average of the smaller two of these four integers is 8, which of the following represents the maximum possible value of the largest integer?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation

Approach Solution 1 :

There is only one solution approach to this problem.

Given: 0 < a < b < c < d. Notice that a, b, c and d are distinct integers.
The average of four distinct positive integers is 10: a + b + c + d = 4 * 10 = 40
The average of the smaller two of these for integers is 8: a + b = 2 * 8 =16
So, 16 + c + d = 40, which leads to c + d = 24
We want to maximize d, so we should minimize c. the minimum value of c is 10.for a = 7 and b = 9.
So, 10 + d = 24 and d = 14

Correct Answer: B

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