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Senior Manager  V
Joined: 02 Jan 2017
Posts: 293
Is xy > 0? (1) x – y > –5 (2) x – 2y < –7  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 66% (02:23) correct 34% (02:12) wrong based on 180 sessions

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Is xy > 0?

(1) x – y > –5
(2) x – 2y < –7
Manager  S
Joined: 13 Apr 2010
Posts: 88
Re: Is xy > 0? (1) x – y > –5 (2) x – 2y < –7  [#permalink]

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vikasp99 wrote:
Is xy > 0?
(1) x – y > –5
(2) x – 2y < –7

Question is asking whether x , y have equal signs .

Individually the statements are not sufficient .
Combining , statement 1 and 2 we get

-x + y < 5
x - 2y < - 7
---------------
-y < -2 = > y > 2

Substituting in one of the equation we get , x > -3
Not sufficient (x can be positive or negative) .

Answer is E .
CEO  V
Joined: 12 Sep 2015
Posts: 3990
Re: Is xy > 0? (1) x – y > –5 (2) x – 2y < –7  [#permalink]

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vikasp99 wrote:
Is xy > 0?

(1) x – y > –5
(2) x – 2y < –7

Great question!

Target question: Is xy > 0

Statement 1: x – y > –5
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 = 1 and y = 1, in which case xy = (1)(1) = 1. So, xy > 0
Case b: x = 1 and y = -1, in which case xy = (1)(-1) = -1. So, xy < 0
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 – 2y < –7
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. So, xy > 0
Case b: x = -10 and y = 1, in which case xy = (-10)(1) = -10. So, xy < 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x – y > –5, which we can rewrite as -5 < x - y
Statement 2 tells us that x – 2y < –7
Since -7 < -5, we can COMBINE the inequalities to get: x – 2y < –7 < -5 < x - y
Focus on x – 2y < x - y
Subtract x from both sides: -2y < -y
Add 2y to both sides: 0 < y
So, y is POSITIVE, but there's no info about x.
Consider these two conflicting scenarios:
Case a: x = 2 and y = 5, in which case xy = (2)(5) = 10. So, xy > 0
Case b: x = -1 and y = 3.5, in which case xy = (-1)(3.5) = -3.5. So, xy < 0
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

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Joined: 26 Mar 2013
Posts: 2341
Re: Is xy > 0? (1) x – y > –5 (2) x – 2y < –7  [#permalink]

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GMATPrepNow wrote:

Target question: Is xy > 0

Statement 1: x – y > –5
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 = 1 and y = 1, in which case xy = (1)(1) = 1. So, xy > 0
Case b: x = 1 and y = -1, in which case xy = (1)(-1) = -1. So, xy < 0
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 – 2y < –7
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. So, xy > 0
Case b: x = -10 and y = 1, in which case xy = (-10)(1) = -10. So, xy < 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x – y > –5, which we can rewrite as -5 < x - y
Statement 2 tells us that x – 2y < –7
Since -7 < -5, we can COMBINE the inequalities to get: x – 2y < –7 < -5 < x - y
Focus on x – 2y < x - y
Subtract x from both sides: -2y < -y
Add 2y to both sides: 0 < y
So, y is POSITIVE, but there's no info about x.
Consider these two conflicting scenarios:
Case a: x = 2 and y = 5, in which case xy = (2)(5) = 10. So, xy > 0
Case b: x = -1 and y = 3.5, in which case xy = (-1)(3.5) = -3.5. So, xy < 0
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

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Dear Brent,

I did it another way:

x – y > –5
x – 2y < –7 ------As both inequality have opposite sign, it is perfect for subtraction.
----------------

y>2 .........So I know 'y 'is Positive and larger than 2. No info about 'x'.. Insufficient

Is my reasoning valid? It gives different answer than you. Can you help please?

Thanks
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Joined: 12 Sep 2015
Posts: 3990
Re: Is xy > 0? (1) x – y > –5 (2) x – 2y < –7  [#permalink]

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Top Contributor
Hi Mo2men,

That's perfect reasoning.

Cheers,
Brent
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Re: Is xy > 0? (1) x – y > –5 (2) x – 2y < –7  [#permalink]

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vikasp99 wrote:
Is xy > 0?

(1) x – y > –5
(2) x – 2y < –7

We need to determine whether x and y are the same sign.

Statement One Alone:

x – y > –5

When x = 10 and y = 14, xy > 0; however, when x = -3 and y = 1, xy < 0. Statement one is not sufficient to answer the question.

Statement Two Alone:

x – 2y < –7

When x = 1 and y = 5, xy > 0; however, when x = -6 and y = 1, xy < 0. Statement two is not sufficient to answer the question.

Statements One and Two Together:

Looking at the statements together, we can first rewrite the inequality from statement one as:

-5 < x - y

Adding that to x - 2y < -7, we have:

-5 + x - 2y < -7 + x - y

-5 - 2y < -7 - y

2 < y

Furthermore, inequality one x - y > -5 means x > y - 5 and inequality two x - 2y < -7 means x < 2y - 7.

Therefore, if y = 4, x > 4 - 5 = -1 and x < 2(4) - 7 = 1. So x can be any number between -1 and 1.

If x = -0.5, then xy = -2 is not greater than 0. On the other hand, if x = 0.5, then xy = 2 is greater than 0.

We see that even with both statements, it’s still not sufficient to answer the question.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: Is xy > 0? (1) x – y > –5 (2) x – 2y < –7   [#permalink] 27 Jan 2019, 19:37
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