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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: 4715
GPA: 3.82

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20 Dec 2017, 23:45
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Difficulty:

25% (medium)

Question Stats:

71% (01:10) correct 29% (00:59) wrong based on 52 sessions

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[GMAT math practice question]

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

1) $$y=|x|$$
2) $$y=-x$$
[Reveal] Spoiler: OA

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Joined: 25 Feb 2013
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21 Dec 2017, 01:56
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
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Re: If x<-1, is √(-x)|x|y=1? [#permalink]

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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.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4715
GPA: 3.82
Re: If x<-1, is √(-x)|x|y=1? [#permalink]

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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.

Note: D is most likely to be the answer if conditions 1) and 2) are equivalent.

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Re: If x<-1, is √(-x)|x|y=1?   [#permalink] 25 Dec 2017, 16:58
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