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

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

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New post 06 Feb 2017, 07:49
1
1
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

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

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

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New post 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.
Answer: E

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

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

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

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New post 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.

Answer: E
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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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