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

It is currently 21 Apr 2019, 21:15

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 > y? (1) 1/x < 1/y (2) 1/x > 1

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54401
Is x > y? (1) 1/x < 1/y (2) 1/x > 1  [#permalink]

Show Tags

New post 21 Nov 2016, 02:42
1
3
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

58% (01:50) correct 42% (01:32) wrong based on 120 sessions

HideShow timer Statistics

Intern
Intern
avatar
Joined: 21 Sep 2016
Posts: 4
Re: Is x > y? (1) 1/x < 1/y (2) 1/x > 1  [#permalink]

Show Tags

New post 21 Nov 2016, 11:56
(1) is not sufficient as we cannot decide from the inequality whether x and y are positive or not.

(2) gives x to be positive and less than 1. But is insufficient to answer the question.

(1,2) gives 0<x<1. Let's take x to be 1/2
=> 1/y > 2
=> y has to be positive, and y < 1/2, or y < x.
Therefore together they are sufficient.

Answer is C.


Sent from my iPad using GMAT Club Forum mobile app
Manager
Manager
avatar
B
Joined: 03 Oct 2013
Posts: 84
Re: Is x > y? (1) 1/x < 1/y (2) 1/x > 1  [#permalink]

Show Tags

New post 21 Nov 2016, 12:47
Statement (1) would be sufficient when we know if x and y are positive or negative.

Statement (2) gives 0<x<1 but nothing about y.

Together we can get the soultion
_________________
P.S. Don't forget to give Kudos on the left if you like the solution
Senior SC Moderator
User avatar
V
Joined: 14 Nov 2016
Posts: 1319
Location: Malaysia
GMAT ToolKit User
Is x > y? (1) 1/x < 1/y (2) 1/x > 1  [#permalink]

Show Tags

New post 22 Feb 2017, 22:15
Bunuel wrote:
Is \(x> y\)?

(1) \(\frac{1}{x} < \frac{1}{y}\)

(2) \(\frac{1}{x} > 1\)


Official solution from Veritas Prep.

This inequality problem fairly clearly includes the concept of reciprocals, but less conspicuously invokes the concept of positive/negative number properties. With statement 1, the "obvious" cases seem to support that \(x>y.\) If you take the statement that \(\frac{1}{x}<\frac{1}{y}\) and plug in \(x=3\) and \(y=2\), that holds with the statement \(\frac{1}{3}<\frac{1}{2}\) and means that \(x>y\). And if both variables are negative, the same can hold. For \(\frac{1}{x} <\frac{1}{y}\) to hold where x and y are negative, then \(\frac{1}{x}\) has to be farther from zero. So that might look like \(x=−2\) and \(y=−3\), where x is still greater than y. But think of a case where the x term will always be smaller than the y term: where x is negative and y is positive. Then the process of taking reciprocals doesn't matter: \(\frac{1}{x}\) is going to still be negative, and \(\frac{1}{y}\) is still going to be positive. So in this case, you get the answer "no," that x is not greater than y. So statement 1 is not sufficient, and that is because of the fact that x could be negative while y is positive.

Statement 2 alone is certainly not sufficient, as it does not provide enough information about y. You know from this statement that \(0<x<1\), because the reciprocal of x is greater than 1. But y still has infinite possibilities.However, when you take the statements together, statement 2 rules out the "exception" for statement 1. It guarantees that x is positive, meaning that both x and y are positive. And that then allows you to simply cross-multiply without changing the sign (since there are no negatives in that multiplication). \(\frac{1}{x} <\frac{1}{y}\) then becomes \(y<x\), proving that the answer is "yes" and making C the correct response.
_________________
"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Advanced Search : https://gmatclub.com/forum/advanced-search/
Intern
Intern
avatar
Joined: 01 Jun 2017
Posts: 2
Is x>y?  [#permalink]

Show Tags

New post 20 Jul 2017, 06:44
Is x>y?

(1) \(\frac{1}{x} < \frac{1}{y}\)
(2) \(\frac{1}{x} > 1\)



Having a problem with the OA. The answer provided is
But they don't consider the possibility of y being a non-integer... I feel like I am probably missing something obvious but it has always been my understanding that one could not assume anything with DS questions.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54401
Re: Is x > y? (1) 1/x < 1/y (2) 1/x > 1  [#permalink]

Show Tags

New post 20 Jul 2017, 06:57
1
1
natesalzman wrote:
Is x>y?

(1) \(\frac{1}{x} < \frac{1}{y}\)
(2) \(\frac{1}{x} > 1\)



Having a problem with the OA. The answer provided is
But they don't consider the possibility of y being a non-integer... I feel like I am probably missing something obvious but it has always been my understanding that one could not assume anything with DS questions.


To answer your question, please check alternative solution below.

Is x>y?

(1) \(\frac{1}{x} < \frac{1}{y}\). If x and y have the same sign, then when cross-multiplying we'll get y < x but if x and y have the opposite signs, when cross-multiplying we'll get y > x. Not sufficient.

(2) \(\frac{1}{x} > 1\). Clearly insufficient because we know nothing about y. Though from this statement we can get that x must be positive.

(1)+(2) Since from (2) x is positive, then from (1) we'll get that (positive) < 1/y, which would mean that y must also be positive. Therefore, when cross-multiplying \(\frac{1}{x} < \frac{1}{y}\), we'll get y < x. Sufficient.

Answer: C.
_________________
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 5807
Location: United States (CA)
Re: Is x > y? (1) 1/x < 1/y (2) 1/x > 1  [#permalink]

Show Tags

New post 30 Jul 2017, 17:43
Bunuel wrote:
Is x > y?

(1) 1/x < 1/y

(2) 1/x > 1


We need to determine whether x is greater than y.

Statement One Alone:

1/x < 1/y

Statement one alone is not sufficient to answer the question. We see that if x = -2 and y = 4, then x is less than y. On the other hand, if x = 1/2 and y = 1/4, then x is greater than y.

Statement Two Alone:

1/x > 1

Since we don’t know anything about y, statement two is not sufficient to answer the question.

Statements One and Two Together:

Using the information from statement two, we see that x must be positive. Thus, we can reciprocate both sides of the inequality and switch the inequality sign:

1/x > 1

x < 1

Using the information from statement one, we see that y has to be positive if x is positive. Thus, we can reciprocate both sides of the inequality and switch the inequality sign:

1/x < 1/y

x > y

We see that x is indeed greater than y.

Answer: C
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

GMAT Club Bot
Re: Is x > y? (1) 1/x < 1/y (2) 1/x > 1   [#permalink] 30 Jul 2017, 17:43
Display posts from previous: Sort by

Is x > y? (1) 1/x < 1/y (2) 1/x > 1

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.