Is xy> 0?
(1) x - y > -2
(2) x - 2y < -6
xy > 0? GMAT Prep
This topic has expert replies
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Statement 1: x > y-2Is 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 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.
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.
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].
Student Review #1
Student Review #2
Student Review #3
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].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
Dear Mitch,GMATGuruNY wrote:Statements 1 and 2 combined:Is xy > 0?
(1) x-y > -2
(2) x-2y < -6
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.
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
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Your approach is perfect!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
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.
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].
Student Review #1
Student Review #2
Student Review #3
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].
Student Review #1
Student Review #2
Student Review #3
- MartyMurray
- Legendary Member
- Posts: 2131
- Joined: Mon Feb 03, 2014 9:26 am
- Location: https://martymurraycoaching.com/
- Thanked: 955 times
- Followed by:140 members
- GMAT Score:800
What you did is perfect.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
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/
Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
You can also subtract inequalities whose signs point the same way too, by flipping the inequality.You can subtract inequalities whose signs point opposite ways.