GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Nov 2018, 12:14

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

November 22, 2018

November 22, 2018

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
• ### Key Strategies to Master GMAT SC

November 24, 2018

November 24, 2018

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

# Is x^2-y^2 < x-y?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6535
GMAT 1: 760 Q51 V42
GPA: 3.82
Is x^2-y^2 < x-y?  [#permalink]

### Show Tags

Updated on: 08 Dec 2017, 00:03
00:00

Difficulty:

65% (hard)

Question Stats:

58% (02:05) correct 42% (01:45) wrong based on 56 sessions

### HideShow timer Statistics

[GMAT math practice question]

Is $$x^2-y^2 < x-y?$$

1) $$x - y < 0$$
2) $$x + y > 0$$

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 06 Dec 2017, 00:08. Last edited by MathRevolution on 08 Dec 2017, 00:03, edited 1 time in total. Intern Joined: 26 Oct 2017 Posts: 27 Re: Is x^2-y^2 < x-y? [#permalink] ### Show Tags 06 Dec 2017, 00:15 Attachment: IMG_20171206_134445.jpg [ 47.83 KiB | Viewed 556 times ] Imo E please correct me if I am wrong in my approach. Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app Manager Joined: 09 Nov 2013 Posts: 80 Re: Is x^2-y^2 < x-y? [#permalink] ### Show Tags 06 Dec 2017, 04:00 I think its E. but we can not cancel out (x-y) on both sides of the equation till we know the signs of x and y or x-y not equals to 0. the expression x2-y2< x-y => (x-y)(x+y-1)<0 { transferring x-y to the LHS } Stat #1 x-y < 0. as we do not know the sign of (x+y-1) we can not conclude that (x-y)(x+y-1)<0 so insuff Stat #2 x+y >0 tells that (x+y-1) will be +ve if x+y>1 and -ve if 0< (x+y) < 1 so insuff Even both the equations do not convey the sign of (x+y-1) to conclude that x2-y2< x-y or (x-y)(x+y-1)<0 thanks Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6535 GMAT 1: 760 Q51 V42 GPA: 3.82 Is x^2-y^2 < x-y? [#permalink] ### Show Tags Updated on: 10 Dec 2017, 22:21 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA method is to modify the original condition and the question, and then recheck the question. Modifying the question yields $$x^2-y^2 < x-y?$$ $$⇔ x^2 - y^2 – ( x - y ) < 0?$$ $$⇔ ( x + y )( x – y ) – ( x - y ) < 0?$$ $$⇔ ( x + y – 1 )( x – y ) < 0?$$ Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer, and so we should consider conditions 1) & 2) together first. Conditions 1) & 2) Since $$x – y < 0$$, asking if $$( x + y – 1 )( x – y ) < 0$$ is equivalent to asking if $$x + y – 1 > 0$$. For $$x = 1, y = 1, x + y – 1 > 0$$ and the answer is ‘yes’. For $$x = \frac{1}{4}$$, $$y = \frac{1}{4}$$, $$x + y – 1 < 0$$ and the answer is ‘no’. Thus, both conditions together are not sufficient. Therefore, the answer is E. In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Originally posted by MathRevolution on 08 Dec 2017, 00:04.
Last edited by MathRevolution on 10 Dec 2017, 22:21, edited 1 time in total.
DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1375
Location: India
Re: Is x^2-y^2 < x-y?  [#permalink]

### Show Tags

08 Dec 2017, 09:37
MathRevolution wrote:
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA method is to modify the original condition and the question, and then recheck the question.

Modifying the question yields
$$x^2-y^2 < x-y?$$
$$⇔ x^2 - y^2 – ( x - y ) < 0?$$
$$⇔ ( x + y )( x – y ) – ( x - y ) < 0?$$
$$⇔ ( x + y – 1 )( x – y ) < 0?$$

Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer, and so we should consider conditions 1) & 2) together first.

Conditions 1) & 2)
Since $$x – y < 0$$, asking if $$( x + y – 1 )( x – y ) < 0$$ is equivalent to asking if $$x + y – 1 > 0$$.
For $$x = 1, y = 1, x + y – 1 > 0$$ and the answer is ‘yes’.
For $$x = \frac{1}{4}$$, $$y = \frac{1}{4}$$, $$x + y – 1 < 0$$ and the answer is ‘no’.

Thus, both conditions together are not sufficient.

Therefore, the answer is E.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.

Hi

In your post, your answer says E (before the last paragraph of your post) as well as C (in the end). And in the question, OA is C. Can you please rectify this.
Re: Is x^2-y^2 < x-y? &nbs [#permalink] 08 Dec 2017, 09:37
Display posts from previous: Sort by

# Is x^2-y^2 < x-y?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.