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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