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

 It is currently 17 Feb 2020, 14:26

### 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 (r^2)x>0?

 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: 8563
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

20 Jun 2016, 16:50
00:00

Difficulty:

55% (hard)

Question Stats:

44% (00:51) correct 56% (00:41) wrong based on 195 sessions

### HideShow timer Statistics

Is (r^2)x>0?
1) r^5=1
2) x>0

*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" Math Expert Joined: 02 Aug 2009 Posts: 8268 Re: Is (r^2)x>0? [#permalink] ### Show Tags 20 Jun 2016, 20:04 1 1 MathRevolution wrote: Is (r^2)x>0? 1) r^5=1 2) x>0 *An answer will be posted in 2 days. Hi, $$(r^2)x>0$$... Here r^2 will always be POSITIVE or ZERO... so we have to know following... a) Is r "0 or non-zero "? b) Is x +, - or zero? lets see the statements- 1) r^5=1 we know r is non-zero.. But nothing about x... If x is + ans is YES otherwise NO.. Insuff 2) x>0 we know x is+, but nothing about r.. If r is 0, ans is NO otherwise YES Insuff combined- r is non-zero and x >0 so ans is YES irrespective of actual values.. Suff C _________________ Current Student Joined: 18 Oct 2014 Posts: 784 Location: United States GMAT 1: 660 Q49 V31 GPA: 3.98 Re: Is (r^2)x>0? [#permalink] ### Show Tags 21 Jun 2016, 10:26 MathRevolution wrote: Is (r^2)x>0? 1) r^5=1 2) x>0 *An answer will be posted in 2 days. For (r^2)x>0, we need to fulfill two conditions:- either r or s must not be 0 x>0 because r^2 will always be +ve 1) r^5=1 r= 1 (as it carries odd power). But there is no information about x. Not sufficient. 2) x>0 No information about r. not sufficient. Combining both statements fulfills our conditions. Hence sufficient. C is the answer _________________ I welcome critical analysis of my post!! That will help me reach 700+ SVP Joined: 23 Feb 2015 Posts: 1538 Re: Is (r^2)x>0? [#permalink] ### Show Tags 21 Jun 2016, 22:23 MathRevolution wrote: Is (r^2)x>0? 1) r^5=1 2) x>0 *An answer will be posted in 2 days. in the question stem r may be (0,+) and x may be (0,+,-) if r=0, then x=0(NO), +(NO), -(NO) again, if r=+, then x=0(NO), +(yes), -(NO) 1) r=(+), but there is no information about x. so, insufficient 2) x>0, but there is no information about r. so, insufficient combining 1 and 2: r=(+) and x=(+)..........YES (sufficient) answer is "C". Thanks... Manager Joined: 18 Jan 2010 Posts: 238 Re: Is (r^2)x>0? [#permalink] ### Show Tags 21 Jun 2016, 23:13 MathRevolution wrote: Is (r^2)x>0? 1) r^5=1 2) x>0 *An answer will be posted in 2 days. r^2 is always a positive value unless r = 0. Statement 1 says r is not equal to zero. But it is silent on x. x could be zero, or negative, then entire value will be zero or negative. If x is positive, entire value will be positive So not sufficient Statement 2 is silent on r. Not sufficient. When we combine, we know that x is not equal to zero and r^2 is always positive. So confirmed "Yes" can be said against the question. C is the answer. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8563 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is (r^2)x>0? [#permalink] ### Show Tags 22 Jun 2016, 19:40 There are two variables (r and x) in the original condition. In order to match the number of variables and the number of equations, we need 2 equations. Hence, the correct answer is C. - 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. _________________ 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"
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4320
Re: Is (r^2)x>0?  [#permalink]

### Show Tags

24 Jun 2016, 10:32
Top Contributor
1
MathRevolution wrote:
Is (r²)x>0?
1) r⁵ = 1
2) x > 0

*An answer will be posted in 2 days.

Target question: Is (r²)(x) > 0?

Statement 1: r⁵ = 1
This tells us that r = 1, however we don't know the value of x.
Let's TEST some values.
Case a: r = 1 and x = 1, in which case (r²)(x) = (1²)(1) = 1. Here, (r²)(x) is GREATER than 0
Case b: r = 1 and x = -1, in which case (r²)(x) = (1²)(-1) = -1. Here, (r²)(x) is NOT GREATER than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x > 0
Okay, x is POSITIVE, however we don't know the value of r.
Let's TEST some values.
Case a: r = 1 and x = 1, in which case (r²)(x) = (1²)(1) = 1. Here, (r²)(x) is GREATER than 0
Case b: r = 0 and x = 1, in which case (0²)(x) = (0²)(1) = 0. Here, (r²)(x) is NOT GREATER than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that r = 1, which means r² = 1
Statement 2 tells us that x is POSITIVE
This means that (r²)(x) = (1³)(POSITIVE) = SOME POSITVE #. In other words, (r²)(x) is GREATER than 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Non-Human User
Joined: 09 Sep 2013
Posts: 14071
Re: Is (r^2)x>0?  [#permalink]

### Show Tags

13 Apr 2019, 09:06
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 (r^2)x>0?   [#permalink] 13 Apr 2019, 09:06
Display posts from previous: Sort by

# Is (r^2)x>0?

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

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