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# Is (r^2)x>0?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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20 Jun 2016, 17:50
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Difficulty:

55% (hard)

Question Stats:

44% (00:50) correct 56% (00:42) wrong based on 190 sessions

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

*An answer will be posted in 2 days.

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"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: 7959 Re: Is (r^2)x>0? [#permalink] ### Show Tags 20 Jun 2016, 21:04 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: 804 Location: United States GMAT 1: 660 Q49 V31 GPA: 3.98 Re: Is (r^2)x>0? [#permalink] ### Show Tags 21 Jun 2016, 11:26 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+ VP Joined: 23 Feb 2015 Posts: 1257 Re: Is (r^2)x>0? [#permalink] ### Show Tags 21 Jun 2016, 23:23 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... _________________ “The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” Henry Wadsworth Longfellow Do you need official questions for Quant? 3700 Unique Official GMAT Quant Questions ------ SEARCH FOR ALL TAGS GMAT Club Tests Manager Joined: 18 Jan 2010 Posts: 246 Re: Is (r^2)x>0? [#permalink] ### Show Tags 22 Jun 2016, 00:13 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: 8011 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is (r^2)x>0? [#permalink] ### Show Tags 22 Jun 2016, 20:40 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"
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24 Jun 2016, 11:32
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
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13 Apr 2019, 10:06
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Re: Is (r^2)x>0?   [#permalink] 13 Apr 2019, 10:06
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