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# Let x=(1/3)^-1/2, y=(1/2)^-1/3, and z=(1/4)^-1/4.

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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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Let x=(1/3)^-1/2, y=(1/2)^-1/3, and z=(1/4)^-1/4.  [#permalink]

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27 Mar 2018, 02:19
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:42) correct 42% (01:47) wrong based on 57 sessions

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[GMAT math practice question]

Let $$x=(\frac{1}{3})^{\frac{-1}{2}}$$, $$y=(\frac{1}{2})^{-\frac{1}{3}}$$, and $$z=(\frac{1}{4})^{\frac{-1}{4}}$$. Which of the following is true?

$$A. x<y<z$$
$$B. z<y<x$$
$$C. x<z<y$$
$$D. y<z<x$$
$$E. y<x<z$$

_________________
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" RC Moderator Joined: 24 Aug 2016 Posts: 789 GMAT 1: 540 Q49 V16 GMAT 2: 680 Q49 V33 Re: Let x=(1/3)^-1/2, y=(1/2)^-1/3, and z=(1/4)^-1/4. [#permalink] ### Show Tags 27 Mar 2018, 07:49 1 1 MathRevolution wrote: [GMAT math practice question] Let $$x=(\frac{1}{3})^\frac{-1}{2}$$, $$y=(\frac{1}{2})^-\frac{1}{3}$$, and $$z=(\frac{1}{4})^\frac{-1}{4}$$. Which of the following is true? $$A. x<y<z$$ $$B. z<y<x$$ $$C. x<z<y$$ $$D. y<z<x$$ $$E. y<x<z$$ $$x=(\frac{1}{3})^\frac{-1}{2}$$ = $$1/\frac{1}{3}^\frac{1}{2}$$ = $$1/\frac{1}{\sqrt{3}}$$ = $$\sqrt{3}$$ = 1.7 approx Similarly , $$y=(\frac{1}{2})^-\frac{1}{3}$$ = $$\sqrt[3]{2}$$ = 1.2 approx And, and $$z=(\frac{1}{4})^\frac{-1}{4}$$ = $$\sqrt[4]{4}$$ = $$\sqrt[2]{2}$$ =1.4 approx Hence , y<z<x ans D _________________ Please let me know if I am going in wrong direction. Thanks in appreciation. Intern Joined: 13 May 2017 Posts: 2 Re: Let x=(1/3)^-1/2, y=(1/2)^-1/3, and z=(1/4)^-1/4. [#permalink] ### Show Tags 28 Mar 2018, 12:00 As nobody could really calculate the squares you just have to simplify them: x = (1/3)^(-1/2) = 3^(1/2) y = (1/2)^(-1/3) = 2^(1/3) z = (1/4)^(-1/4) = 4^(1/4) = 2^(1/2) I think now it's easy to sort them by size. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8029 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Let x=(1/3)^-1/2, y=(1/2)^-1/3, and z=(1/4)^-1/4. [#permalink] ### Show Tags 29 Mar 2018, 01:12 2 => We raise each of $$x, y$$, and $$z$$ to the exponent $$12$$ as this will yield integers that are easily compared. $$x^{12} = ((\frac{1}{3})^{\frac{-1}{2}})^{12} = ((3)^{\frac{1}{2}})^{12} = 3^6 = 729$$ $$y^{12} = ((\frac{1}{2})^{\frac{-1}{3}})^{12} = ((2)^{\frac{1}{3}})^{12} = 2^4 = 16$$ $$z^{12} = ((\frac{1}{4})^{\frac{-1}{4}})^{12} = ((4)^{\frac{1}{4}})^{12} = 4^3 = 64$$ We have $$y^{12} < z^{12} < z^{12}$$. Since $$x, y$$, and $$z$$ are all positive, this tells use that $$y < z < x.$$ Therefore, the answer is D. 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$79 for 1 month Online Course"
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Re: Let x=(1/3)^-1/2, y=(1/2)^-1/3, and z=(1/4)^-1/4.   [#permalink] 29 Mar 2018, 01:12
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