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# Is xy > 1 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 50000
Is xy > 1 ?  [#permalink]

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27 Feb 2017, 04:30
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Question Stats:

82% (01:12) correct 18% (00:44) wrong based on 26 sessions

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Is xy > 1 ?

(1) x/y > 1
(2) x ≥ 1 and y > 2

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Manager
Joined: 13 Apr 2010
Posts: 89
Re: Is xy > 1 ?  [#permalink]

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27 Feb 2017, 07:10
Bunuel wrote:
Is xy > 1 ?

(1) x/y > 1
(2) x ≥ 1 and y > 2

For Statement 1 :
Consider values x = 5 , y = 2 ; 5/2 = 2.5
so, xy > 1 (Yes)

Consider values x = 1/2 , y = 1/3 ; 3/2 = 1.5
so, xy > 1 (No)

Statement 2 :
We can definitely answer xy> 1
so , it is Sufficient

CEO
Joined: 12 Sep 2015
Posts: 3012
Re: Is xy > 1 ?  [#permalink]

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27 Feb 2017, 09:50
Top Contributor
Bunuel wrote:
Is xy > 1 ?

(1) x/y > 1
(2) x ≥ 1 and y > 2

Target question: Is xy > 1 ?

Statement 1: x/y > 1
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 2 ans y = 1 (so x/y = 2/1 = 2. So, x/y > 1). In this case, xy = (2)(1) = 2. So, xy > 1
Case b: x = 2 ans y = 0.1 (so x/y = 2/0.1 = 20. So, x/y > 1). In this case, xy = (2)(0.1) = 0.2. So, xy < 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: x ≥ 1 and y > 2
If x ≥ 1 and y > 2, then x and y are both positive, which means xy is POSITIVE
More importantly, since x ≥ 1 and y > 2, we know that the SMALLEST value of xy is when x = 1 and when y is just a TINY BIT bigger than 2, which we'll denote as 2+ (a number a bit bigger than 2).
In this case, xy = (1)(2+) = 2+
So, the SMALLEST possible value of xy is 2+, which means xy is definitely greater than 1.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
_________________

Brent Hanneson – GMATPrepNow.com

Re: Is xy > 1 ? &nbs [#permalink] 27 Feb 2017, 09:50
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