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## Set S = {1, 2, 3, 4, 5, 6, 7, x} If x is an integer

tagged by: VJesus12

This topic has 1 expert reply and 0 member replies

### Top Member

VJesus12 Master | Next Rank: 500 Posts
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#### Set S = {1, 2, 3, 4, 5, 6, 7, x} If x is an integer

Sat Feb 10, 2018 1:27 am
Set S = {1, 2, 3, 4, 5, 6, 7, x}

If x is an integer, which of the following could be the median of Set S?

A. 3.75
B. 4.25
C. 4.5
D. 5
E. 5.25

The OA is the option C.

How can I find the median without knowing the value of x? Should I assume that x>7? I am a little confused.

Experts, may you help me? Thanks in advanced.

### GMAT/MBA Expert

EconomistGMATTutor GMAT Instructor
Joined
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Sun Feb 11, 2018 3:03 am
VJesus12 wrote:
Set S = {1, 2, 3, 4, 5, 6, 7, x}

If x is an integer, which of the following could be the median of Set S?

A. 3.75
B. 4.25
C. 4.5
D. 5
E. 5.25

The OA is the option C.

How can I find the median without knowing the value of x? Should I assume that x>7? I am a little confused.

Experts, may you help me? Thanks in advanced.
Hello Vjesus12.

Since all the numbers are sorted, we can assume that x>7.

Now, as the set S has an even number of elements (8), the median is given by (a+b)/2, where "a" and "b" are the numbers on the middle of the set.

In our case, a=4 and b=5. Therefore, the median is $$M=\frac{4+5}{2}=\frac{9}{2}=4.5.$$ This is why the correct answer is the option C=4.5.

Feel free to ask me again if you have a doubt.

Regards.

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