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# If 0 < x < 1, which of the following is the greatest?

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Math Expert
Joined: 02 Sep 2009
Posts: 46284
If 0 < x < 1, which of the following is the greatest? [#permalink]

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10 Sep 2017, 05:10
00:00

Difficulty:

35% (medium)

Question Stats:

54% (00:55) correct 46% (00:34) wrong based on 54 sessions

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If 0 < x < 1, which of the following is the greatest?

A. $$x^{(-\frac{1}{2})}$$

B. $$x^0$$

C. $$x^{(\frac{1}{2})}$$

D. $$x^1$$

E. $$x^2$$

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Manager
Joined: 12 Feb 2017
Posts: 71
If 0 < x < 1, which of the following is the greatest? [#permalink]

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10 Sep 2017, 09:58
1
0 < x < 1
lets assume x=0.16

A)x^(-1/2)
=1/{x^(1/2)}
=1/(0.16)^1/2
=1/0.4
=2.5

B)x^0=1

c)x^1/2
=0.16^1/2
=0.4

D)x^1
=0.16^1
=0.16

E)x^2
=0.16^2
=0.0256

Kudos if it helps.
SC Moderator
Joined: 22 May 2016
Posts: 1759
If 0 < x < 1, which of the following is the greatest? [#permalink]

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10 Sep 2017, 14:09
Bunuel wrote:
If 0 < x < 1, which of the following is the greatest?

A. $$x^{(-\frac{1}{2})}$$

B. $$x^0$$

C. $$x^{(\frac{1}{2})}$$

D. $$x^1$$

E. $$x^2$$

If 0 < x < 1, it is a proper fraction, (e.g., $$\frac{1}{2}$$).

Number properties
If very fluent in properties of these fractions, finding the answer is quick and no calculations are needed:

The negative exponent with the smallest value will yield the greatest answer. Only choice A has a negative exponent.

Given their equal absolute values, you could compare Answer A and Answer C (see below for calculation) to be sure.

After that or at a glance, the greatest result is

Test a value

Because the answer choices contain square roots, and to keep things simple, choose a unit fraction whose denominator is a perfect square, e.g. $$\frac{1}{9}$$

A. $$(\frac{1}{9})^{(-\frac{1}{2})}$$ =$$9^{(\frac{1}{2})}$$ = $$\sqrt{9} = 3$$

B. $$(\frac{1}{9})^0$$ = 1

C.$$(\frac{1}{9})^{(\frac{1}{2})}$$ =$$\sqrt{\frac{1}{9}}$$ = $$\frac{1}{3}$$

D. $$(\frac{1}{9})^1$$ = $$\frac{1}{9}$$

E. $$(\frac{1}{9})^2$$ = $$\frac{1}{81}$$

Greatest of these results?

_________________

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If 0 < x < 1, which of the following is the greatest?   [#permalink] 10 Sep 2017, 14:09
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