xy > 0? GMAT Prep

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xy > 0? GMAT Prep

by prata » Fri Jun 24, 2016 11:05 pm
Is xy> 0?

(1) x - y > -2

(2) x - 2y < -6

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by GMATGuruNY » Sat Jun 25, 2016 2:59 am
Is xy > 0?

(1) x-y > -2
(2) x-2y < -6
Statement 1: x > y-2
If y=2 and x= 1, is 1*2 > 0? YES.
If y= -1 and x = 1, is (1)(-1) > 0? NO.
Since the answer is YES in the first case but NO in the second case, INSUFFICIENT.

Statement 2: x < 2y-6
If y=1 and x = -10, is (1)(-10) > 0? NO.
If y = 10 and x = 1, is 1*10 > 0? YES.
Since the answer is NO in the first case but YES in the second case, INSUFFICIENT.

Statements 1 and 2 combined:
Linking together the two statements, we get:
y-2 < x < 2y-6
y-2 < 2y-6
4 < y
y > 4.
Since y > 4 and x > y-2, we know that x > 2.
Thus, xy > 0.
SUFFICIENT.

The correct answer is C.
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by [email protected] » Sat Jun 25, 2016 8:29 am
Hi prata,

This DS question is perfect for TESTing VALUES.

We're asked if XY > 0? This is a YES/NO question.

Fact 1: X - Y > - 2

This can rewritten as:

X + 2 > Y

If X = 1, Y = 1, XY = 1 and the answer to the question is YES
If X = 1, Y = 0, XY = 0 and the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: X - 2Y < -6

This can be rewritten as:

X + 6 < 2Y

If X = 0, Y = 4, then XY = 0 and the answer to the question is NO
If X = 1, Y = 4, then XY = 4 and the answer to the question is YES
Fact 2 is INSUFFICIENT

Combined, we know:
X + 2 > Y
X + 6 < 2Y

2Y - 6 > X > Y - 2

From this, with a bit of "tinkering", we can deduce that...

Y CANNOT be 0, since -6 > X > -2 is impossible
Y CANNOT be negative (it would create the same "impossible" situation)

Since 2Y - 6 > Y - 2
2Y - Y > -2 + 6

Y MUST be > 4

Since Y > 4...

X + 2 > 4

X MUST be > 2

This means that X and Y are BOTH POSITIVE, so the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

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by evs.teja » Tue Jun 28, 2016 2:44 pm
GMATGuruNY wrote:
Is xy > 0?

(1) x-y > -2
(2) x-2y < -6
Statements 1 and 2 combined:
Linking together the two statements, we get:
y-2 < x < 2y-6
y-2 < 2y-6
4 < y
y > 4.
Since y > 4 and x > y-2, we know that x > 2.
Thus, xy > 0.
SUFFICIENT.

The correct answer is C.
Dear Mitch,
I solved this question in this way
x-y>-2
-x +2y > 6

=>> on adding both equations y>4

Was I lucky or we can do such transformation to get the right ans ?

Regards
Teja

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by GMATGuruNY » Tue Jun 28, 2016 3:21 pm
evs.teja wrote:Dear Mitch,
I solved this question in this way
x-y>-2
-x +2y > 6

=>> on adding both equations y>4

Was I lucky or we can do such transformation to get the right ans ?

Regards
Teja
Your approach is perfect!
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
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by MartyMurray » Tue Jun 28, 2016 3:40 pm
evs.teja wrote:I solved this question in this way
x-y>-2
-x +2y > 6

=>> on adding both equations y>4

Was I lucky or we can do such transformation to get the right ans ?

Regards
Teja
What you did is perfect.

You can add inequalities whose signs point the same way.

You can subtract inequalities whose signs point opposite ways.

For more information and explanation along with some practice problems, check this out.

https://magoosh.com/gmat/2013/gmat-quant ... qualities/
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by Matt@VeritasPrep » Fri Jul 22, 2016 2:37 am
You can subtract inequalities whose signs point opposite ways.
You can also subtract inequalities whose signs point the same way too, by flipping the inequality. :)