Is XY > 0?
(1) X - Y > -2
(2) X - 2Y < -6
DS Inequality Practice
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Statement 1: x > y-2tonebeeze wrote:Is XY > 0?
(1) X - Y > -2
(2) X - 2Y < -6
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 can both Yes and No, 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 can be both No and Yes, insufficient.
Statements 1 and 2 combined:
Linking together the two statements, we get:
y-2 < x < 2y-6
y-2 < 2y-6
y > 4.
Since y > 4 and x > y-2, we know that x > 2.
Thus, x and y are both positive.
Sufficient.
The correct answer is C.
Last edited by GMATGuruNY on Tue May 03, 2011 8:18 am, edited 3 times in total.
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- MAAJ
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I got different values for x and y, but both are positive. Would someone tell me where am I wrong?
Here's what I did:
x - y > -2
-x + 2y > 6 (Note: x - 2y < -6 mutiplied by -1)
y > 4
x - 2y < -6
-2x + 2y < 4 (Note: x - y > -2 multiplied by -2)
-x < -2 Thus x > 2
I got y > 4 and x > 2 are these values correct?
Here's what I did:
x - y > -2
-x + 2y > 6 (Note: x - 2y < -6 mutiplied by -1)
y > 4
x - 2y < -6
-2x + 2y < 4 (Note: x - y > -2 multiplied by -2)
-x < -2 Thus x > 2
I got y > 4 and x > 2 are these values correct?
"There's a difference between interest and commitment. When you're interested in doing something, you do it only when circumstance permit. When you're committed to something, you accept no excuses, only results."
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It looks as though you submitted your post as I was editing a typo in mine. We got the same results.MAAJ wrote:I got different values for x and y, but both are positive. Would someone tell me where am I wrong?
Here's what I did:
x - y > -2
-x + 2y > 6 (Note: x - 2y < -6 mutiplied by -1)
y > 4
x - 2y < -6
-2x + 2y < 4 (Note: x - y > -2 multiplied by -2)
-x < -2 Thus x > 2
I got y > 4 and x > 2 are these values correct?
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
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.
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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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- MAAJ
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Oh thanks!
"There's a difference between interest and commitment. When you're interested in doing something, you do it only when circumstance permit. When you're committed to something, you accept no excuses, only results."
I did solve the question in similar manner. But is it okay to add Y and 2Y (read variables)in above equations even though we don't know their signs?GMATGuruNY wrote:Statement 1: x > y-2tonebeeze wrote:Is XY > 0?
(1) X - Y > -2
(2) X - 2Y < -6
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 can both Yes and No, 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 can be both No and Yes, insufficient.
Statements 1 and 2 combined:
Linking together the two statements, we get:
y-2 < x < 2y-6
y-2 < 2y-6
y > 4.
Since y > 4 and x > y-2, we know that x > 2.
Thus, x and y are both positive.
Sufficient.
The correct answer is C.
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Adding is always fine - your inequalities won't flip.xyzx5230 wrote:I did solve the question in similar manner. But is it okay to add Y and 2Y (read variables)in above equations even though we don't know their signs?
Subtracting is NOT necessarily fine, however - you have to recognize that subtract is like adding by a negative, so your inequality will flip.
For example:
x > y
2x > 3 - y
Adding these together, I get 3x > 3, or x > 1.
But let's say I wanted to subtract one from the other. Many people would do
(x > y)
- (2x > 3 - y)
----------------
-x > 2y - 3
But this is INCORRECT.
(x > y) - (2x > 3 - y) is really
(x > y) + -(2x > 3 - y), or
(x > y) + (-2x < y - 3), or
(x > y)
+ (y - 3 > -2x), or
x + y - 3 > y - 2x, or
x - 3 > -2x, or
3x > 3, or x > 1