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Re: Which of the following CANNOT be the median of the 3 [#permalink]
20 Feb 2012, 23:09

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Praetorian wrote:

Which of the following CANNOT be the median of the 3 positive integers x, y, and z?

A. x B. z C. x+z D. (x+z)/2 E. (x+z)/3

The median of a set with odd number of terms is just a middle term, so it's x, y or z. Eliminate A and B right away. Now, the median can also be (x+z)/2 and (x+z)/3 (for example: {1, 2, 3} and {1, 2, 5}).

But since x, y, and z are positive integers then it no way can be x+z. Why? Because a middle term (the median) cannot possibly be greater than two terms (x and z) in a set with 3 terms.

Answer: C.

Notice that, if we were not told that x, y, and z are positive then x+y could be the median, consider {-1, 0, 1}: -1+1=0=median. _________________

Re: Which of the following CANNOT be the median of the 3 [#permalink]
21 Feb 2012, 00:38

Bunuel wrote:

Praetorian wrote:

Which of the following CANNOT be the median of the 3 positive integers x, y, and z?

A. x B. z C. x+z D. x+z/2 E. x+z/3

The median of a set with odd number of terms is just a middle term, so it's x, y or z. Eliminate A and B right away. Now, the median can also be (x+y)/2 and (x+y)/3 (for example: {1, 2, 3} and {1, 2, 5}).

But since x, y, and z are positive integers then it no way can be x+y. Why? Because a middle term (the median) cannot possibly be greater than two terms (x and y) in a set with 3 terms.

Answer: C.

Notice that, if we were not told that x, y, and z are positive then x+y could be the median, consider {-1, 0, 1}: -1+1=0=median.

Just out of curiosity, is it always to be assumed that the variables are distinct integers? i.e. would there be cases where a gmat question names variables x, y, z without explicitly stating that theyre "distinct" ?

Re: Which of the following CANNOT be the median of the 3 [#permalink]
21 Feb 2012, 00:41

Expert's post

essarr wrote:

Just out of curiosity, is it always to be assumed that the variables are distinct integers? i.e. would there be cases where a gmat question names variables x, y, z without explicitly stating that theyre "distinct" ?

No, we should not assume that. For example here x, y, and z can be the same integer. _________________

Re: Which of the following CANNOT be the median of the 3 [#permalink]
26 May 2013, 08:01

If x=1, y=2, z=1 then by (C) x+z=2 which is y But I suppose trick is to remember the median is the "middle value", when variables are arranged in ascending/descending order

Re: Which of the following CANNOT be the median of the 3 [#permalink]
16 Jun 2013, 06:10

1

This post received KUDOS

Bunuel wrote:

Praetorian wrote:

Which of the following CANNOT be the median of the 3 positive integers x, y, and z?

A. x B. z C. x+z D. x+z/2 E. x+z/3

The median of a set with odd number of terms is just a middle term, so it's x, y or z. Eliminate A and B right away. Now, the median can also be (x+y)/2 and (x+y)/3 (for example: {1, 2, 3} and {1, 2, 5}).

But since x, y, and z are positive integers then it no way can be x+y. Why? Because a middle term (the median) cannot possibly be greater than two terms (x and y) in a set with 3 terms.

Answer: C.

Notice that, if we were not told that x, y, and z are positive then x+y could be the median, consider {-1, 0, 1}: -1+1=0=median.

You have assumed x+z/2 ==( x+z)/2. I really see the question as unclear. Should there be brackets?

Re: Which of the following CANNOT be the median of the 3 [#permalink]
16 Jun 2013, 06:57

Expert's post

AbuRashid wrote:

Bunuel wrote:

Praetorian wrote:

Which of the following CANNOT be the median of the 3 positive integers x, y, and z?

A. x B. z C. x+z D. x+z/2 E. x+z/3

The median of a set with odd number of terms is just a middle term, so it's x, y or z. Eliminate A and B right away. Now, the median can also be (x+y)/2 and (x+y)/3 (for example: {1, 2, 3} and {1, 2, 5}).

But since x, y, and z are positive integers then it no way can be x+y. Why? Because a middle term (the median) cannot possibly be greater than two terms (x and y) in a set with 3 terms.

Answer: C.

Notice that, if we were not told that x, y, and z are positive then x+y could be the median, consider {-1, 0, 1}: -1+1=0=median.

You have assumed x+z/2 ==( x+z)/2. I really see the question as unclear. Should there be brackets?