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

 It is currently 26 Feb 2020, 09:47

### 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

# If x and y are integers, is ax > ay?

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 61508
If x and y are integers, is ax > ay?  [#permalink]

### Show Tags

06 Feb 2017, 06:52
1
6
00:00

Difficulty:

45% (medium)

Question Stats:

61% (01:26) correct 39% (01:45) wrong based on 191 sessions

### HideShow timer Statistics

If x and y are integers, is $$ax > ay$$?

(1) $$a^3*x > a^3*y$$

(2) $$–ax < –ay$$

_________________
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4355
Re: If x and y are integers, is ax > ay?  [#permalink]

### Show Tags

06 Feb 2017, 09:39
5
Top Contributor
1
Bunuel wrote:
If x and y are integers, is ax > ay?

(1) a³x > a³y
(2) –ax < –ay

Great question!

Target question: Is ax > ay?

Given: x and y are integers

Statement 1: a³x > a³y
First recognize that this statement is quite similar to the target question.
Also recognize that, statement 1 tells us that a ≠ 0. This is very useful, because we can now be certain that a² is POSITIVE
If a² is POSITIVE, we can safely take the inequality a³x > a³y and divide both sides by a² to get: ax > ay
Perfect! This answers the target question.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: –ax < –ay
Let's multiply both sides of the inequality to get: ax > ay [Aside: since we multiplied both sides of the inequality by a NEGATIVE value, we reversed the direction of the inequality sign]
Perfect! Once again, we have answered the target question.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

RELATED VIDEO

_________________
Test confidently with gmatprepnow.com
##### General Discussion
Director
Joined: 05 Mar 2015
Posts: 956
Re: If x and y are integers, is ax > ay?  [#permalink]

### Show Tags

06 Feb 2017, 09:46
Bunuel wrote:
If x and y are integers, is ax > ay?

(1) a^3*x > a^3*y
(2) –ax < –ay

seems D is the answer

(1) a^3(x-y)>0
as a and a^3 ,both has same signs thus a(x-y) >0
suff

(2) –ax < –ay
-a(x-y)<0
thus if a is positive than (x-y) also positive so suff
or, if a is negative then (x-y) negative too thus a(x-y)>0
suff

Ans D
Intern
Joined: 20 Jun 2017
Posts: 6
Re: If x and y are integers, is ax > ay?  [#permalink]

### Show Tags

31 Oct 2017, 09:37
Sir, from statement 1 how can we conclude that a^2 is positive
Math Expert
Joined: 02 Sep 2009
Posts: 61508
Re: If x and y are integers, is ax > ay?  [#permalink]

### Show Tags

31 Oct 2017, 09:42
Raj94* wrote:
Sir, from statement 1 how can we conclude that a^2 is positive

The square of a number (more generally an even power of a number) is always non-negative, so 0 or positive. $$a^3*x > a^3*y$$ also implies that $$a \neq 0$$, becasue if it were, then we'd have $$a^3*x =0 = a^3*y$$. Thus, in this a^2 is not only non-negative but positive.
_________________
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8601
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If x and y are integers, is ax > ay?  [#permalink]

### Show Tags

02 Nov 2017, 09:43
1
Bunuel wrote:
If x and y are integers, is $$ax > ay$$?

(1) $$a^3*x > a^3*y$$

(2) $$–ax < –ay$$

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations. We can modify the original condition and question as follows.

$$ax > ay <=> a^3x > a^3y$$ if $$a≠0$$.
$$ax > ay <=> -ax < -ay$$.

Condition 1)
Since $$a^3x > a^3y$$, $$a$$ is not zero.
By dividing both sides by $$a^2$$, we have $$ax > ay$$ since $$a^2 > 0$$.
This is sufficient.

Conditin 2)
By multiplying $$-ax < -ay$$ by $$-1$$, we have $$ax > ay$$.
This is sufficient.

Happy Studying !!!
_________________
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"
Intern
Joined: 08 Aug 2018
Posts: 40
Location: India
GMAT 1: 720 Q49 V40
GPA: 4
WE: Engineering (Energy and Utilities)
Re: If x and y are integers, is ax > ay?  [#permalink]

### Show Tags

28 Oct 2018, 23:25
1
GMATPrepNow wrote:
Bunuel wrote:
If x and y are integers, is ax > ay?

(1) a³x > a³y
(2) –ax < –ay

Great question!

Target question: Is ax > ay?

Given: x and y are integers

Statement 1: a³x > a³y
First recognize that this statement is quite similar to the target question.
Also recognize that, statement 1 tells us that a ≠ 0. This is very useful, because we can now be certain that a² is POSITIVE
If a² is POSITIVE, we can safely take the inequality a³x > a³y and divide both sides by a² to get: ax > ay
Perfect! This answers the target question.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: –ax < –ay
Let's multiply both sides of the inequality to get: ax > ay [Aside: since we multiplied both sides of the inequality by a NEGATIVE value, we reversed the direction of the inequality sign]
Perfect! Once again, we have answered the target question.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

RELATED VIDEO

What if a is negative? Will statement 2 still hold?
Non-Human User
Joined: 09 Sep 2013
Posts: 14143
Re: If x and y are integers, is ax > ay?  [#permalink]

### Show Tags

19 Feb 2020, 17:51
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If x and y are integers, is ax > ay?   [#permalink] 19 Feb 2020, 17:51
Display posts from previous: Sort by

# If x and y are integers, is ax > ay?

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

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