It is currently 23 Oct 2017, 10:54

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is x<1/y?

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

Hide Tags

Expert Post
Math Revolution GMAT Instructor
User avatar
P
Joined: 16 Aug 2015
Posts: 4155

Kudos [?]: 2923 [0], given: 0

GPA: 3.82
Premium Member CAT Tests
Is x<1/y? [#permalink]

Show Tags

New post 24 Aug 2016, 19:21
Expert's post
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

58% (00:57) correct 42% (00:46) wrong based on 132 sessions

HideShow timer Statistics

Is x<1/y?
1) y>0
2) xy<1

*An answer will be posted in 2 days.
[Reveal] Spoiler: OA

_________________

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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Kudos [?]: 2923 [0], given: 0

Top Contributor
Senior Manager
Senior Manager
avatar
Joined: 15 Sep 2011
Posts: 358

Kudos [?]: 405 [0], given: 45

Location: United States
WE: Corporate Finance (Manufacturing)
GMAT ToolKit User
Re: Is x<1/y? [#permalink]

Show Tags

New post 24 Aug 2016, 19:38
Top Contributor
There is no information about x or y so nothing can be done to reduce the initial statement...at first.

Statement 1: y>0, explains nothing about x. NSUF
Statement 2: xy<1, x and y could be different signs or x and y could be fractions or a combination of the two. NSUF

Statement 1 & 2: if y>0 and xy<1 then divide the equation by y and you have the statement. SUF

Kudos [?]: 405 [0], given: 45

Intern
Intern
avatar
Joined: 27 Dec 2010
Posts: 4

Kudos [?]: [0], given: 0

Re: Is x<1/y? [#permalink]

Show Tags

New post 25 Aug 2016, 15:36
S1)\(y>0\)

Pick \(y=1\) and \(x=2\);
=>\(2<\frac{1}{1}\)
=>No

Pick \(y=2\) and \(x=-2\)
=>\(-2<\frac{1}{2}\)
=>Yes

So S1 is insufficient

BCE

S2)\(xy<1\)

Pick \(x=\frac{1}{2}\) and \(y=\frac{1}{2}\)
=>\(\frac{1}{2}<2\)
=> Yes

Pick \(x=\frac{1}{2}\) and \(y=\frac{-1}{2}\)
=>\(\frac{1}{2}<-2\)
=>No

So S2 is insufficient (Note: This statement could be a trap if inequality in question stem is just cross multiplied without checking possible values that \(y\) could take.)

CE

S1 and S2)

Pick \(x=\frac{1}{2}\) and \(y=\frac{1}{2}\);This meets both the statements
=>\(\frac{1}{2}<2\)
=>Yes

Pick \(x=-2\) and \(y=1\); This meets both the statements
=> \(-2<\frac{1}{1}\)
=>Yes

Here \(y>0\) is satisfied from statement 1; both positive and negative values (integer and fraction as well) for \(x\) are tried and that should cover all possible values for \(x\) and the output is an YES in both the cases. Hence Statements 1 and 2 taken together is sufficient. Answer is C.

(S1 says that \(y>0\); So if \(y\), which is greater than 0, is divided both sides of statement 2, then it will not change the sign of the inequality and we get \(x<\frac{1}{y}\) which is exactly what the question stem is asking. Hence C)

Kudos [?]: [0], given: 0

Expert Post
Top Contributor
1 KUDOS received
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1798

Kudos [?]: 2476 [1], given: 357

Location: Canada
Re: Is x<1/y? [#permalink]

Show Tags

New post 26 Aug 2016, 06:08
1
This post received
KUDOS
Expert's post
Top Contributor
3
This post was
BOOKMARKED
MathRevolution wrote:
Is x < 1/y?

1) y > 0
2) xy < 1



Target question: Is x < 1/y?

Statement 1: y > 0
No information about x, so statement 1 is NOT SUFFICIENT

Statement 2: xy < 1
IMPORTANT: some students will want to divide both sides by y to get x < 1/y, HOWEVER doing so is incorrect, because we don't know whether y is POSITIVE or NEGATIVE.
If y is POSITIVE, then dividing both sides by y gives us x < 1/y
If y is NEGATIVE, then dividing both sides by y gives us x > 1/y [when we divide both sides by a negative value, we must REVERSE the direction of the inequality]
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that y is POSITIVE
Statement 2 tells us that xy < 1
Since we know that y is POSITIVE, we can safely divide both sides by y to get the inequality x < 1/y.

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

Answer =
[Reveal] Spoiler:
C


RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2476 [1], given: 357

Expert Post
Math Revolution GMAT Instructor
User avatar
P
Joined: 16 Aug 2015
Posts: 4155

Kudos [?]: 2923 [0], given: 0

GPA: 3.82
Premium Member CAT Tests
Re: Is x<1/y? [#permalink]

Show Tags

New post 27 Aug 2016, 05:21
If we modify the original condition and the question, in case of inequality, square is very important. If we multiply y^2 to both sides, we get xy^2<y?, xy^2-y<0?, y(xy-1)<0?. There are 2 variables (x and y) and there is a high chance that C is the correct answer. Using 1) & 2), the answer is always yes and the condition is sufficient. Thus, the correct answer is C.

_________________

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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Kudos [?]: 2923 [0], given: 0

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16534

Kudos [?]: 274 [0], given: 0

Premium Member
Re: Is x<1/y? [#permalink]

Show Tags

New post 09 Sep 2017, 14:57
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 274 [0], given: 0

Re: Is x<1/y?   [#permalink] 09 Sep 2017, 14:57
Display posts from previous: Sort by

Is x<1/y?

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.