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# Is xy > 3 ? (1) x + y > 3 (2) x – y > 3

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Joined: 02 Sep 2009
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Is xy > 3 ? (1) x + y > 3 (2) x – y > 3  [#permalink]

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06 Feb 2017, 07:49
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Difficulty:

45% (medium)

Question Stats:

64% (01:51) correct 36% (01:38) wrong based on 38 sessions

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Is xy > 3 ?

(1) x + y > 3
(2) x – y > 3

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CEO
Joined: 12 Sep 2015
Posts: 3011
Re: Is xy > 3 ? (1) x + y > 3 (2) x – y > 3  [#permalink]

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06 Feb 2017, 10:07
Top Contributor
Bunuel wrote:
Is xy > 3 ?

(1) x + y > 3
(2) x – y > 3

Target question: Is xy > 3 ?

Statement 1: x + y > 3
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 = 10 and y = 1, in which case xy = (10)(1) = 10. In other words, xy > 3
Case b: x = 4 and y = 0.5, in which case xy = (4)(0.5) = 2. In other words, xy < 3
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, you can read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: x - y > 3
This statement doesn't FEEL sufficient either, so I'll TEST some values.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 10 and y = 1, in which case xy = (10)(1) = 10. In other words, xy > 3
Case b: x = 4 and y = 0.5, in which case xy = (4)(0.5) = 2. In other words, xy < 3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Since I was able to use the SAME x-values and y-values in the two statements above to show the individual statements were not sufficient, we can conclude that the COMBINED statements are not sufficient.

To clarify, the following cases satisfy the conditions of BOTH statements.
Case a: x = 10 and y = 1, in which case xy = (10)(1) = 10. In other words, xy > 3
Case b: x = 4 and y = 0.5, in which case xy = (4)(0.5) = 2. In other words, xy < 3
Since we cannot answer the target question with certainty, the statement COMBINED are NOT SUFFICIENT

Cheers,
Brent
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Brent Hanneson – GMATPrepNow.com

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Re: Is xy > 3 ? (1) x + y > 3 (2) x – y > 3  [#permalink]

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09 Feb 2017, 04:34
x & y are just 2 variables, not necessarily integers.

Looking at st1 & st2, one after the another, we cannot predict the product range of 2 variables if just the sum or the difference of the 2 variables is given

For ex. x=5; y=6 --> x+y > 3 and xy > 3.
Now, x= 0, y = 4 -- > x+y >3 and xy <3.
Insufficient.

Similar case can be made for the difference
For ex. x=9; y=2 --> x-y > 3 and xy > 3.
Now, x= 4, y = 0 -- > x-y >3 and xy <3.
Insufficient.

Combining the 2 statements, I get x > 3.
Note that since we cannot subtract the inequality, because we don't know the signs of x or y, we cannot conclude anything about the range of y.

So even after combining, insufficient.
So, E.

Bunuel wrote:
Is xy > 3 ?

(1) x + y > 3
(2) x – y > 3
Intern
Joined: 15 Oct 2014
Posts: 17
Re: Is xy > 3 ? (1) x + y > 3 (2) x – y > 3  [#permalink]

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09 Feb 2017, 06:10
Since statement 1 or 2 alone is not sufficient I follow the below approach please guide whether I am wright or wrong.
(x+y)^2>9 from statement 1 and
(x-y)^2>9 from statement 2 subtracting both we get xy>0 hence not sufficient.

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Posts: 2830
Re: Is xy > 3 ? (1) x + y > 3 (2) x – y > 3  [#permalink]

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13 Feb 2017, 17:16
Bunuel wrote:
Is xy > 3 ?

(1) x + y > 3
(2) x – y > 3

We need to determine whether xy > 3.

Statement One Alone:

x + y > 3

Statement one alone is not sufficient to answer the question. For instance, if x = 1/2 and y = 3, then xy = 3/2 IS NOT greater than 3. However, if x = 2 and y = 3, then xy = 6 IS greater than 3.

Statement Two Alone:

x – y > 3

Statement two alone is not sufficient to answer the question. For instance, if x = 4 and y =1/2, then xy = 2 IS NOT greater than 3. However, if x = 5 and y = 1, then xy = 5 IS greater than 3.

Statements One and Two Together:

If we add the two inequalities from statements one and two, we will have:

(x + y > 3)

+ (x - y > 3)

2x > 6

x > 3

However, this still is not enough information to answer the question.

For instance, if if x = 4 and y =1/2, then xy IS NOT greater than 3. However, if x = 5 and y = 1, then xy IS greater than 3.

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Re: Is xy > 3 ? (1) x + y > 3 (2) x – y > 3 &nbs [#permalink] 13 Feb 2017, 17:16
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