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# If x<-1, is √(-x)|x|y=1?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6815
GMAT 1: 760 Q51 V42
GPA: 3.82

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20 Dec 2017, 23:45
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Difficulty:

45% (medium)

Question Stats:

61% (01:36) correct 39% (01:46) wrong based on 124 sessions

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[GMAT math practice question]

If $$x<-1$$, is $$\sqrt{(-x)|x|}$$$$/y=1$$?

1) $$y=|x|$$
2) $$y=-x$$

_________________

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 $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Retired Moderator Joined: 25 Feb 2013 Posts: 1220 Location: India GPA: 3.82 If x<-1, is √(-x)|x|y=1? [#permalink] ### Show Tags 21 Dec 2017, 01:56 2 MathRevolution wrote: [GMAT math practice question] If $$x<-1$$, is $$\sqrt{(-x)|x|}$$$$/y=1$$? 1) $$y=|x|$$ 2) $$y=-x$$ $$\sqrt{(-x)|x|}$$$$/y=1$$. Square both sides to get $$(-x)|x|=y^2$$. Now as $$x<-1$$ i.e negative so $$|x|=-x$$ therefore, the question stem Is $$(-x)(-x)=y^2 => x^2=y^2$$ ? Statement 1: $$y=|x|$$, square both sides to get $$y^2=x^2$$. Sufficient Statement 2: $$y=-x$$, square both sides to get $$y^2=x^2$$. Sufficient Option D ------------------------------------------------------------- Alternatively, assume some values for x and test the stem Statement 1: let $$x=-2$$ so $$y=|-2|=2$$ Question stem $$\sqrt{-(-2)|-2|}=y=>\sqrt{4}=y =>y=2$$ . Sufficient Statement 2: let $$x=-2$$ so $$y=-(-2)=2$$. Same as statement 1. Sufficient DS Forum Moderator Joined: 21 Aug 2013 Posts: 1432 Location: India Re: If x<-1, is √(-x)|x|y=1? [#permalink] ### Show Tags 21 Dec 2017, 08:11 MathRevolution wrote: [GMAT math practice question] If $$x<-1$$, is $$\sqrt{(-x)|x|}$$$$/y=1$$? 1) $$y=|x|$$ 2) $$y=-x$$ x < -1, so we know x is a negative number. Lets say x = -a, where 'a' is positive (so for example if x=-3 then a becomes 3, if x =-1.2, then a becomes 1.2). So -x becomes -(-a) = a and |x| also becomes a. So LHS = √(a*a)/y = a/y. and RHS =1. So the question is asking us if a/y = 1 OR is y = a? (1) y = |x| and |x| = a (since x = -a), so y = a. Sufficient. (2) y = -x = -(-a) = a. Sufficient. Hence D answer Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6815 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x<-1, is √(-x)|x|y=1? [#permalink] ### Show Tags 25 Dec 2017, 16:58 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question. Modifying the question: Since x<-1, x is negative and we have |x| = -x. So, $$\sqrt{(-x)|x|}/y=1$$ $$⇔\sqrt{(-x)(-x)}/y=1$$ $$⇔\sqrt{x^2}/y=1$$ $$⇔|x|/y=1$$ $$⇔-x/y=1$$ $$⇔ y=-x$$ Condition 1) $$y=|x|$$ $$⇔ y=-x$$ Since this is equivalent to the question, condition 1) is sufficient. Condition 2) Since this is also equivalent to the question, condition 2) is sufficient too. The answer is D. Note: D is most likely to be the answer if conditions 1) and 2) are equivalent. Answer: D _________________ 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$149 for 3 month Online Course"
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Re: If x<-1, is √(-x)|x|y=1? &nbs [#permalink] 25 Dec 2017, 16:58
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