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If X is an integer, is Y an integer? (1) The average

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If X is an integer, is Y an integer? (1) The average [#permalink] New post 06 Dec 2003, 22:02
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"If X is an integer, is Y an integer?

(1) The average (arithmetic mean) of X and Y is not an integer.

(2) X + Y = 2 (X - Y)
Statement 1 alone is sufficient but Statement 2 alone is NOT.
Statement 2 alone is sufficient but Statement 1 alone is NOT.
Statements 1 and 2 TOGETHER are sufficient but neither alone is.
EACH statement alone is sufficient,
NEITHER statement alone or combined is sufficient.
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 [#permalink] New post 06 Dec 2003, 22:23
Quote:
"If X is an integer, is Y an integer?


Quote:
(1) The average (arithmetic mean) of X and Y is not an integer.


Insufficient.X and Y could be 1 and 2, for example.

Quote:
(2) X + Y = 2 (X - Y)

X+Y=2X-2Y
X+3Y=2X
X=3Y

Insufficient. If X is 1, Y is 1/3. If X is 3, Y is 1.

But, together, every combination of X and Y that satisfies condition 2 (examples):
X Y
3 1
6 2
9 3

Averages to an integer.

There are no (integer, integer) pairs that satisfy both conditions.

I say C.
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 [#permalink] New post 06 Dec 2003, 22:26
Also, to satisfy condition 1, you need an even and an odd.

To satisfy condition 2, you need two odds or two evens.

No pair of integers can satisfy both conditions.

So I suppose that's a better shortcut.
  [#permalink] 06 Dec 2003, 22:26
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