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If xy < 4, is x < 2 ?

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Source: — Data Sufficiency |

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by Anurag@Gurome » Sun Mar 18, 2012 5:11 am
pappueshwar wrote:If xy < 4, is x < 2 ?

(1) y > 1
(2) y > x

OA IS B.
(1) y > 1
If x = 5/2, y = 3/2, then xy = 15/4, which is less than 4. Here x > 2.
If x = 1, y = 3/2, then xy = 3/2, which is less than 4. Here x < 2.
No definite answer; NOT sufficient.

(2) y > x
If x = 3/2, y = 5/2, then xy = 15/4, which is less than 4. Here x < 2.
If x = 1, y = 3/2, then xy = 3/2, which is less than 4. Here x < 2.
Generalizing we can see that if we take x > 2, say x = 2.1, then xy cannot be less than 4 for a value of y such that y > x, so it will be a contradiction as y > x and xy < 4. So, we know that x < 2 always; SUFFICIENT.

The correct answer is B.
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by pappueshwar » Sun Mar 18, 2012 5:42 am
that was grt expln.

thanks
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by ameya85 » Mon Mar 19, 2012 12:22 am
Anurag@Gurome wrote:
pappueshwar wrote:If xy < 4, is x < 2 ?

(1) y > 1
(2) y > x

OA IS B.
(1) y > 1
If x = 5/2, y = 3/2, then xy = 15/4, which is less than 4. Here x > 2.
If x = 1, y = 3/2, then xy = 3/2, which is less than 4. Here x < 2.
No definite answer; NOT sufficient.

(2) y > x
If x = 3/2, y = 5/2, then xy = 15/4, which is less than 4. Here x < 2.
If x = 1, y = 3/2, then xy = 3/2, which is less than 4. Here x < 2.
Generalizing we can see that if we take x > 2, say x = 2.1, then xy cannot be less than 4 for a value of y such that y > x, so it will be a contradiction as y > x and xy < 4. So, we know that x < 2 always; SUFFICIENT.

The correct answer is B.
Dear Anurag,

I re-phrased the question. Please tell me where I have made the mistake.

xy<4 --> x<4/y
is 4/y > 2?
is y>2?
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by GMATGuruNY » Mon Mar 19, 2012 4:28 am
pappueshwar wrote:If xy < 4, is x < 2 ?

(1) y > 1
(2) y > x

OA IS B.
Statement 1: y > 1 (and, from the question stem, xy<4)
It's possible that y=3/2 and that x=5/2.
It's possible that y=2 and that x=0.
Since in the first case x>2, and in the second case x<2, INSUFFICIENT.

Statement 2: y>x (and, from the question stem, xy<4)
It's possible that y=2 and that x=0.
Our only concern now is what happens if x>0.
If x>0:
Since xy < 4, y < 4/x.
Since x < y and y < 4/x, x < 4/x.
Thus, x² < 4, implying that x<2.
SUFFICIENT.

The correct answer is B.
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