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

 It is currently 20 Oct 2019, 22:56 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

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

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

Hide Tags

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8023
GMAT 1: 760 Q51 V42 GPA: 3.82

Show Tags

1
9 00:00

Difficulty:   45% (medium)

Question Stats: 61% (01:26) correct 39% (01:22) wrong based on 201 sessions

HideShow timer Statistics

Is x>y?

1) x+a>x-a
2) ax>ay

_________________
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4015

Show Tags

5
Top Contributor
MathRevolution wrote:
Is x > y?

1) x + a > x - a
2) ax > ay

Target question: Is x > y?

Statement 1: x + a > x - a
This statement doesn't include any information about y, so there's no way to answer the target question.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: ax > ay
Some students will divide both sides by a and incorrectly conclude that x > y.
However, before we divide by a variable, we must ensure that the variable is EITHER positive OR negative, because if we divide by a negative value, we must reverse the direction of the inequality, and if we divide by a positive value, the direction of the inequality stays the same. As it stands, we don't know whether a is positive or negative.

To see what I mean, consider these values of a, x and y that satisfy the given condition:
Case a: a = 1, x = 3 and y = 2, in which case x > y
Case b: a = -1, x = 2 and y = 3, in which case x < y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x + a > x - a
Add a to both sides to get: x + 2a > x
Subtract x from both sides to get: 2a > 0
Divide both sides by 2 to get: a > 0. In other words, a is POSITIVE

Statement 2 tells us that ax > ay
Now that we know that a is POSITIVE, we can take ax > ay and safely divide both sides by a to get: x > y
PERFECT!
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

RELATED VIDEO FROM OUR COURSE

_________________
General Discussion
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8023
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Is x>y?  [#permalink]

Show Tags

==> In the original condition, there are 2 variables (x, y) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), from con 1), you get a>-a, 2a>0, or a>0, and from con 2), you get ax>ay, and the inequality sign doesn’t change even if you divide both sides by a because since a>9, you get x>y, hence yes, it is always sufficient.

Therefore, the answer is C.
_________________
Intern  B
Joined: 12 Aug 2016
Posts: 7

Show Tags

MathRevolution wrote:
Is x > y?

1) x + a > x - a
2) ax > ay

Target question: Is x > y?

Statement 1: x + a > x - a
a + a > x - x
2a > 0
a > 0
a is POSITIVE
That's all this statement tells us.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT.

Statement 2: ax > ay
ax - ay > 0
a(x - y) > 0
Case a: a > 0 and (x - y) > 0, in which case x > y
Case b: a < 0 and (x - y) < 0, in which case x < y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT.

Statements 1 and 2 combined
Statement 1 tells us that a is POSITIVE

Statement 2 tells us that, if a > 0, x > y

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Non-Human User Joined: 09 Sep 2013
Posts: 13321
Re: Is x>y?  [#permalink]

Show Tags

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: Is x>y?   [#permalink] 24 Jan 2019, 07:00
Display posts from previous: Sort by

Is x>y?

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

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