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# GRE Math Challenge #143- The median of 10, 15, x, and y is 1

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GRE Math Challenge #143- The median of 10, 15, x, and y is 1 [#permalink]  15 May 2015, 11:44
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Question Stats:

100% (00:55) correct 0% (00:00) wrong based on 8 sessions
The median of 10, 15, x, and y is 18.5, and x<y.

 Quantity A Quantity B X 22

• Quantity A is greater.
• Quantity B is greater.
• Both Quantities are Equal
• Cannot be determined
[Reveal] Spoiler: OA

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Re: GRE Math Challenge #143- The median of 10, 15, x, and y is 1 [#permalink]  09 Dec 2016, 02:20
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Re: GRE Math Challenge #143- The median of 10, 15, x, and y is 1 [#permalink]  09 Dec 2016, 08:13
Expert's post
The given set is 10 15 x and y and x is less than y.

Now clearly x > 15 otherwise the median of the set would be $$\frac{(10+15)}{2}$$=12.5

So the set is 10, 15, x and y. The median is $$\frac{(x+15)}{2}$$=18.5

so $$x+15=18.5*2$$ or $$x=37-15 =22$$.

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Re: GRE Math Challenge #143- The median of 10, 15, x, and y is 1 [#permalink]  15 Dec 2016, 22:16
Another way to think about it: The median number of a given set must always be the middle number of the set. In a set with odd numbers, let's say 5 in the set, the median will always be the third number ordered in the set. In this case, because the set has four numbers, the middle number will be exactly halfway between 15 and x, because 15 is the second number in the set and x must be the third number. We know that the median (the halfway point) is 18.5, which is 3.5 more than 15. Therefore the number x must be 3.5 more than 18.5, which is 22. So it is Answer C.
Re: GRE Math Challenge #143- The median of 10, 15, x, and y is 1   [#permalink] 15 Dec 2016, 22:16
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