BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Is xy > 0

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 324
Joined: Mon Jul 05, 2010 6:44 am
Location: London
Thanked: 70 times
Followed by:3 members

by kmittal82 » Tue Aug 24, 2010 6:52 am
(1)

x - y > -2

=> x > y - 2

Various values of x and y satisfy the above, some yielding xy as +ve, some as -ve.. Not sufficient

(2)

x - 2y < -6

=> 2y - 6 > x

Various values of x and y satisfy this, some yielding xy as +ve, some as -ve. Not Sufficient

Combining:

x - y > -2

=> x - 2y > -2 -y

From (2), we know

x - 2y < -6

Using both, we can say:

-2 -y < -6 => y >4 ( using the logic: b>a, b < c => c > a)

This in turn implies that x has to positive to satisfy x - y > -2 , thus xy will be positive

Hence (C)

Can you confirm the OA?
Top
Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Tue Mar 27, 2012 10:27 pm

by gmaterial » Tue Apr 03, 2012 12:29 pm
The OA is C.
Top
User avatar
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

by GMATGuruNY » Sat Apr 07, 2012 1:01 am
One way to combine the two statements is to link together the inequalities. I posted an explanation here:

https://www.beatthegmat.com/ds-inequalit ... 82218.html
Last edited by GMATGuruNY on Mon Jul 21, 2014 8:12 am, edited 1 time in total.
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
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 134
Joined: Fri Apr 06, 2012 3:11 am
Thanked: 35 times
Followed by:5 members

by Shalabh's Quants » Sat Apr 07, 2012 5:51 am
Hi,

One way could be...

By Stat.1, x-y>-2 => by dividing both sides by -2. => x/-2-y/-2<1 => x/-2+ y/2<1,

If we plot above linear inequality in XY plane. Line passes through (-2,0) & (0,2) points. It means the line passes through 3 quadrants namely 1,2 & 3.

In quadrants 1; The co-ordinate of x & y will be both +ive.
In quadrants 2; The co-ordinate of x & y will be x -ive & y +ive.
In quadrants 3; The co-ordinate of x & y will be both -ive.

so, product of xy would be +ive in quadrants 1&3, or xy>1.
but,product of xy would be -ive in quadrants 2, or xy<1.

hence stat. 1 is insufficient.

Taking stat. 2...

x - 2y < -6
=> by dividing both sides by -6. => x/-6-2y/-6>1
or, x/-6+y/3>1

If we plot above linear inequality in XY plane. Line passes through (-6,0) & (0,3) points. It means this line too passes through 3 quadrants namely 1,2 & 3.

In quadrants 1; The co-ordinate of x & y will be both +ive.
In quadrants 2; The co-ordinate of x & y will be x -ive & y +ive.
In quadrants 3; The co-ordinate of x & y will be both -ive.

so, product of xy would be +ive in quadrants 1&3, or xy>1.
but,product of xy would be -ive in quadrants 2, or xy<1.

hence stat. 2 is insufficient.

Combining both statements... Simply solve 2 inequalities treating them as linear equation.

x-y>-2 & x-2y<-6;

=> x-y>-2
-x+2y>6;(Changing the sign of inequality)

Which yields y>4 & x>2. or xy>1.

hence stat. 1 & 2 together are sufficient.
Shalabh Jain,
e-GMAT Instructor
Top
Junior | Next Rank: 30 Posts
Posts: 10
Joined: Tue Aug 16, 2011 7:32 am

by pims » Mon Jul 21, 2014 6:48 am
Rich ?
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Mon Jul 21, 2014 7:04 am
GMAT Hacker wrote:Is xy > 0 ?

(1) x - y > -2

(2) x - 2y < -6

I will post the QA later.
Target question: Is xy > 0 ?

Statement 1: x - y > -2
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 1 and y = 1, in which case xy > 0
Case b: x = 1 and y = -1, in which case xy < 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x - 2y < -6
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = -10 and y = -1, in which case xy > 0
Case b: x = -10 and y = 1, in which case xy < 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
NOTE: We can ADD inequalities if the inequality signs are facing the SAME DIRECTION.
Statement 1 says x - y > -2
Take statement 2 and multiply both sides by -1 to get: -x + 2y > 6
Now that the inequality signs are facing the SAME DIRECTION, add the inequalities to get:
y > 4
In other words, y is POSITIVE
Also, since y > 4 and x > y-2, we know that x > 2. In other words, x is POSITIVE
If x and y are both POSITIVE, then we can be certain that xy > 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pm
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members

by GMATinsight » Mon Jul 21, 2014 8:03 am
GMAT Hacker wrote:Is xy > 0 ?

(1) x - y > -2

(2) x - 2y < -6

I will post the QA later.
Question : Is XY > 0?
but if X and Y have same Sign then Answer to the question will be YES
and if X and Y have Different Sign then Answer to the question will be NO

Therefore we only have to find out whether their signs are same or not

Question Rephrased : Do X and Y have same Sign?

Statement 1) X-Y > -2
which can be true for X=2 and Y = -1 (X and Y different sign) and also if
which can be true for X=2 and Y = 1 (X and Y same sign)

Inconsistent Solution therefore INSUFFICIENT

Statement 2) X-2Y < -6
which can be true for X=-10 and Y = 1 (X and Y different sign) and also if
which can be true for X=2 and Y = 10 (X and Y same sign)

Inconsistent Solution therefore INSUFFICIENT

Combining the two statements
X-2Y < -6 i.e. -X+2Y >6
and
X-Y > -2

Adding the two equations we get
(-X+2Y)+(X-Y) > 6-2
i.e. Y > 4
i.e. Y is positive
from Statement 1
X-Y > -2
i.e. X > -2+(4)
i.e. X > 2
i.e. X is positive

Both are positive therefore

SUFFICIENT

Answer: Option C
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Top

GMAT/MBA Expert

User avatar
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

by [email protected] » Mon Jul 21, 2014 1:58 pm
Hi pims,

This is a rather "lean" DS question - it has no restrictions; it's just a question. Is XY > 0? This is a YES/NO question.

This is a great question for TESTing VALUES. In these situations, I love using the number 0 (if I'm not restricted from using it by something in the Facts). This question is also built around some Number Properties:

For XY to be greater than 0, then....
X and Y are BOTH positive OR BOTH negative (which gives us a YES answer)

ANY other combination (1 positive and 1 negative, anything and a 0) will give you an XY that is NOT greater than 0 (which gives us a NO answer).

Fact 1: X - Y > -2

Let's TEST VALUES
If....
X = 1, Y = 0, then the answer to the question is NO
X = 1, Y = 1, then the answer to the question is YES
Fact 1 is INSUFFICIENT

Fact 2: X - 2Y < -6

Again, let's TEST VALUES
If...
X = -10, Y = 0, then the answer to the question is NO
X = -10, Y = -1, then the answer to the question is YES
Fact 2 is INSUFFICIENT

Combined, we know...
X - Y > -2
X - 2Y < -6

From here, we can "do math" in a variety of ways. I'm going to rewrite the inequalities....

X > Y - 2
X < 2Y - 6

And then combine them...

2Y - 6 > X > Y - 2

We now know....

2Y - 6 > Y - 2

Simplify...

Y > 4

Plugging that information back into this inequality...

X > Y - 2

X > (>4) - 2

....means that X MUST be POSITIVE.

So, Y is POSITIVE and X is POSITIVE, so the answer to the question is always YES.
Combined, SUFFICIENT.

Final Answer:C

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Post new topic Post Reply
• Page 1 of 1