MGRE exam question doubt

[rao.nischal]

Hi,

One of the questions in one of the CAT test from Manhattan Prep is:

Set S includes elements {8, 2, 11, x, 3, y} and has an average (arithmetic mean) of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?

A: 0
B: 1
C: 2
D: 3
E: 4

The answer provided for this question is D. However, I disagree with the answer. Isn't it true that a Set should contain only unique elements in it. If so, choice D (and C) can be directly eliminated. (Choice B would be the right answer then as per the explanation provided).

Please correct me if I am wrong.

Regards,
Nischal

[tommywallach]

Hey Rao,

Not sure where you're getting that a set of numbers needs to be made up of distinct values. That's definitely not a rule! If you can point me to somewhere in one of the books where we state this, I'll gladly admit the error, but I highly doubt we'd do that! : )

-t

[rao.nischal]

Hi Tommy,

I have not used any of the MGRE maths books, but I remember reading this in the math review of the official guide.

Also, the first sentence in wikipedia's definition (http://en.wikipedia.org/wiki/Set_(mathematics) ) says that a set consists of distinct objects.

I know this is maybe a very minor detail but the GRE has a habit of using these subtle concepts as trap questions.

Thanks,
Nischal

P.S: I finished my GRE today. So any new info provided here will probably help other students.

[tommywallach]

Hey Rao,

It's definitely not the case, and there are numerous examples in all books that make it clear. The Wikipedia page you cite is simply using a different definition of the term; that's why you (and all who are prepping) should make sure to get your rules from GRE books, not general math books. Sometimes there are differences, like this one.

If you look further down that Wikipedia page, you can see why it wouldn't apply here. Plenty of GRE questions say things like:

"Set X is comprised of: 3, 3, 4, 4, 5, x, and 9," so you know they aren't defining it as only distinct integers. Either way, great question. Hope your GRE went well!

-t