Harshgmat wrote:

Which of the 5 terms x, y, x + y, x – 1, and y + 1, represents the median of these 5 terms?

(1) x > y

(2) x – y < 1

Since these expressions are simple to evaluate, I used substitution.

(1) x > y, make x = 2 and y = 1

The (unordered) list becomes: 2, 1, 2 + 1, 2 - 1, 1 + 1 --> 2, 1, 3, 1, 2

Put them in order: 1, 1, 2, 2, 3 --> "2" is the median.

However, "2" could be "x" or "y + 1"

Therefore, I cannot tell which of the five terms is the median. Insufficient.

(2) x - y < 1, make x = 3 and y = 3

Unordered list: 3, 3, 3 + 3, 3 - 1, 3 +1 --> 3, 3, 6, 2, 4

Ordered list: 2, 3, 3, 5, 6 --> "3" is the median

However, "3" could be "x" or "y"

Therefore, I cannot tell which of the five terms is the median. Insufficient.

Now, if I put them together:

x > y and x - y < 1, make x = 3 and y = 2.5

Unordered list: 3, 2.5, 3 + 2.5, 3 - 1, 2.5 + 1 --> 3, 2.5, 5.5, 2, 3.5

Ordered list: 2, 2.5, 3, 3.5, 5.5

"3" is the median, so in this case, "x" is the median.

Try a different case:

Make x = 1/2 and y = -1/4

Unordered list: 1/2, -1/4, 1/2 + (-1/4), 1/2 - 1, -1/4 + 1 --> 1/2, -1/4, 1/4, -1/2, 3/4

Ordered list: -1/2, -1/4, 1/4, 1/2, 3/4

"1/4" is the median, so in this case, "x + y" is the median.

There is still more than one value that could be the median. Both statements together are insufficient.

Answer: E.

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Audra Zook

GMAT and GRE Tutor

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