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

 It is currently 16 Feb 2020, 12:03

### 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

# Is x<1/y?

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

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8556
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

24 Aug 2016, 18:21
2
5
00:00

Difficulty:

55% (hard)

Question Stats:

60% (01:20) correct 40% (01:12) wrong based on 162 sessions

### HideShow timer Statistics

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

*An answer will be posted in 2 days.

_________________
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" Senior Manager Joined: 15 Sep 2011 Posts: 302 Location: United States WE: Corporate Finance (Manufacturing) Re: Is x<1/y? [#permalink] ### Show Tags 24 Aug 2016, 18:38 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 Intern Joined: 27 Dec 2010 Posts: 4 Re: Is x<1/y? [#permalink] ### Show Tags 25 Aug 2016, 14:36 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) GMAT Club Legend Joined: 11 Sep 2015 Posts: 4318 Location: Canada Re: Is x<1/y? [#permalink] ### Show Tags 26 Aug 2016, 05:08 1 Top Contributor 3 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 = RELATED VIDEO _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8556 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x<1/y? [#permalink] ### Show Tags 27 Aug 2016, 04:21 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. "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"
Senior Manager
Joined: 02 Apr 2014
Posts: 457
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34
GPA: 3.5

### Show Tags

12 Dec 2017, 11:28
$$x < 1/y$$ ?
Re-arranging,
=> $$x - (1/y) < 0$$ ?
=> $$(xy - 1)/y < 0$$ ?
For this term to be negative, ($$xy < 1$$ AND $$y > 0$$) OR ($$xy > 1$$ AND $$y < 0$$) ?
Question becomes => ($$xy < 1$$ AND $$y > 0$$) OR ($$xy > 1$$ AND $$y < 0$$) ?

Statement 1: $$y > 0$$, but we don't know if $$xy < 1$$ => InSufficient
Statement 2: $$xy < 1$$, but we don't know if $$y > 0$$ => InSufficient

Statement 1 + 2: $$y > 0$$ AND $$xy < 1$$ => Answers our question

Non-Human User
Joined: 09 Sep 2013
Posts: 14073
Re: Is x<1/y?  [#permalink]

### Show Tags

13 Sep 2019, 11:14
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<1/y?   [#permalink] 13 Sep 2019, 11:14
Display posts from previous: Sort by

# Is x<1/y?

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

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