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

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Intern
Joined: 29 Aug 2003
Posts: 29
Location: Mumbai
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If X is an integer, is Y an integer? (1) The average [#permalink]  06 Dec 2003, 21:02
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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.
Director
Joined: 28 Oct 2003
Posts: 503
Location: 55405
Followers: 1

Kudos [?]: 10 [0], given: 0

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.
Director
Joined: 28 Oct 2003
Posts: 503
Location: 55405
Followers: 1

Kudos [?]: 10 [0], given: 0

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.
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