GMAT Problem Solving- A list of measurements in increasing order is 4, 5, 6, 8, 10 and x

Question: A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If the median of these measurements is 6/7 times their arithmetic mean, what is the value of x?

1. 16
2. 15
3. 14
4. 13
5. 12

“A list of measurements in increasing order is 4, 5, 6, 8, 10 and x.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT 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 approach to solve the problem.

Given:

• A list of measurements in increasing order is 4, 5, 6, 8, 10 and x.

Condition:

• The median of these measurements is 6/7 times their arithmetic mean

Find Out:

• The value of x?

Let us consider the numbers 4, 5, 6, 8, 10, x as per the question.

Median would be the average of two middle terms

--> median = \(\frac{6+8}{2}\) 
--> median = 7

Mean will be:
→  \(\frac{4+5+6+8+10+x}{6}\)
=\(\frac{33+x}{6}\)

As per the given problem statement:
Median is 6/7th time of the arithmetic mean
Hence:

=> median= 6/7 ∗mean
=> 7=6/7 * \(\frac{33+x}{6}\)
=> 49=33+x
=> x=49−33
=> x=16

Correct Answer: A

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