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

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

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

by VJesus12 » 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.

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Source: Beat The GMAT — Problem Solving | Sat Feb 10, 2018 1:27 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » 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.

Let's see your questions.

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 [spoiler]C=4.5[/spoiler].

I hope this answer can help you.

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

Regards.

GMAT Prep From The Economist
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Jun 23, 2019 6:27 pm

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

If x > 4, then the median is the average of 4 and 5, which is 4.5.

Answer: C

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