GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 28 Jan 2020, 11:51

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Is x - x^2 > y - y^2 ? (1) x > y (2) x^2 > y^2

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 60727
Is x - x^2 > y - y^2 ? (1) x > y (2) x^2 > y^2  [#permalink]

Show Tags

New post 06 Dec 2019, 05:50
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

56% (02:19) correct 44% (01:56) wrong based on 57 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
avatar
P
Joined: 25 Jul 2018
Posts: 490
Is x - x^2 > y - y^2 ? (1) x > y (2) x^2 > y^2  [#permalink]

Show Tags

New post 06 Dec 2019, 07:08
Is \(x —x^{2} > y—y^{2}\) ?

Good approach is picking numbers

(Statement1): x > y
—> if 3 > 2, then —6 > —2 (No)
—> if —2 > —3, then —6 > —12(yes)

Insufficient

(Statement2): \(x^{2} > y^{2}\)

If \(3^{2} > 2^{2}\), then —6 > —4 (No)

If \((1.5)^{2} > (—1)^{2}\), then 1.5 —2.25 > —1 —1 —> —0.75 > —2 (Yes)

Insufficient

Taken together 1&2,
The same thing as statement2
Insufficient

The answer is E

Posted from my mobile device
Manager
Manager
avatar
G
Status: Student
Joined: 14 Jul 2019
Posts: 151
Location: United States
Concentration: Accounting, Finance
GPA: 3.9
WE: Education (Accounting)
Is x - x^2 > y - y^2 ? (1) x > y (2) x^2 > y^2  [#permalink]

Show Tags

New post 06 Dec 2019, 19:16
Bunuel wrote:
Is \(x - x^2 > y - y^2\) ?


(1) \(x > y\)

(2) \(x^2 > y^2\)


Are You Up For the Challenge: 700 Level Questions


\(x -x^2 > y -y^2\) = x-y > (x+y) (x-y)

(1) x > y = x- y > 0, so we need to know the sign of x+y. insufficient.

(2) \(x^2 > y^2\) = \(x^2- y^2 > 0\). but we don't know the value of x-y. insufficient

Together, both x - y and \(x^2 -y^2\) is positive. Lets take x as 1/2 and y as 1/4. so, \(x - x^2\) will be (1/2) which is greater than \(y- y ^2 \)will be 3/16. Again when x=3, y =2 , then \(x- x^2\) becomes -6 and \(y -y^2\) becomes -2, so\( x-x^2 < y -y^2\). insufficient.

E is the answer.
Senior Manager
Senior Manager
avatar
G
Joined: 28 Feb 2014
Posts: 283
Location: India
Concentration: General Management, International Business
GMAT 1: 570 Q49 V20
GPA: 3.97
WE: Engineering (Education)
Re: Is x - x^2 > y - y^2 ? (1) x > y (2) x^2 > y^2  [#permalink]

Show Tags

New post 22 Dec 2019, 02:40
Bunuel wrote:
Is \(x - x^2 > y - y^2\) ?


(1) \(x > y\)

(2) \(x^2 > y^2\)


x - x^2 > y - y^2
x - y > x^2 - y^2
x - y > (x - y) (x + y)
(x - y) ( x + y -1) < 0

(1) x > y
x - y >0; ( x + y -1) can be positive or negative. Insufficient

(2) x^2 > y^2; taking square root on both the sides
|x| > |y|; signs of x and y are unknown. Insufficient

(1)+(2) still signs of x and y are unknown. Insufficient

E is correct.
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8475
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Is x - x^2 > y - y^2 ? (1) x > y (2) x^2 > y^2  [#permalink]

Show Tags

New post 22 Dec 2019, 20:51
Bunuel wrote:
Is \(x - x^2 > y - y^2\) ?


(1) \(x > y\)

(2) \(x^2 > y^2\)


Are You Up For the Challenge: 700 Level Questions



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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

The question is equivalent to (x-y)(x+y-1) < 0 for the followings.

\(x - x^2 > y - y^2\)
\(⇔ 0 > x^2 - y^2 - x + y\)
\(⇔ x^2 - y^2 - x + y < 0\)
\(⇔ (x+y)(x-y) - (x-y) < 0\)
\(⇔ (x-y)(x+y-1) < 0\)

Since we have 2 variables (x and y) and 0 equations, C is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

If \(x = 2, y = 1\), then \((x-y)(x+y+1) = 1 \cdot 2 = 2 > 0\) and the answer is 'no'.
If \(x = 2, y = -1.5\), then \((x-y)(x+y-1) = 3.5 \cdot (-0.5) < 0\) and the answer is 'yes'.

Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
_________________
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 $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
GMAT Club Bot
Re: Is x - x^2 > y - y^2 ? (1) x > y (2) x^2 > y^2   [#permalink] 22 Dec 2019, 20:51
Display posts from previous: Sort by

Is x - x^2 > y - y^2 ? (1) x > y (2) x^2 > y^2

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne