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

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Joined: 02 Sep 2009
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If 0 < a < 1, which of the following is the greatest?  [#permalink]

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10 Sep 2017, 05:13
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67% (01:31) correct 33% (01:27) wrong based on 141 sessions

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

A. $$(-2a)^{(-2)}$$

B. $$\frac{1}{a^{(-2)}}$$

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

D. $$a^{(-2)}$$

E. $$a^2$$

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If 0 < a < 1, which of the following is the greatest?  [#permalink]

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10 Sep 2017, 12:55
1
Bunuel wrote:
If 0 < a < 1, which of the following is the greatest?

A. $$(-2a)^{(-2)}$$

B. $$\frac{1}{a^{(-2)}}$$

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

D. $$a^{(-2)}$$

E. $$a^2$$

as $$a$$ is positive and $$a<1$$, so $$\frac{1}{a}>1$$. Hence a fraction where $$a$$ is in the denominator and numerator is $$1$$ will have a value greater than $$1$$. Hence we can straight away eliminate options B, C & E as $$a$$ is in the numerator (essentially option B, C & E are same $$= a^2$$ and as it is given $$a<1$$, so squaring both sides will yield $$a^2<1$$)

Option A: can be written as $$\frac{1}{(2a)^{2}}$$ $$= \frac{1}{4a^2}$$

Option D: can be written as $$\frac{1}{a^2}$$. Multiply the numerator and the denominator by $$4$$. we get
$$\frac{4}{4a^2} > \frac{1}{4a^2}$$

Hence Option D
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If 0 < a < 1, which of the following is the greatest?  [#permalink]

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14 Sep 2017, 11:09
Bunuel wrote:
If 0 < a < 1, which of the following is the greatest?

A. $$(-2a)^{(-2)}$$

B. $$\frac{1}{a^{(-2)}}$$

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

D. $$a^{(-2)}$$

E. $$a^2$$

Let a = $$\frac{1}{4}$$, and evaluate each answer choice. Straight algebra -- reciprocals, fractions, and squares -- became too tangled.

A. $$(-2a)^{(-2)}$$ --> $$\frac{1}{(-2*a)^2}$$

$$\frac{1}{(-2*\frac{1}{4})^2}$$ =

$$\frac{1}{(-\frac{1}{2})^2}$$ = $$\frac{1}{(\frac{1}{4})}$$ = 4

B. $$\frac{1}{a^{(-2)}}$$ --> $$\frac{a^2}{1^2}$$

$$a^2$$ = $$(\frac{1}{4})^2$$ =$$\frac{1}{16}$$

C.$$(\frac{1}{a})^{(-2)}$$ --> $$\frac{a^2}{1^2}$$=

$$a^2$$. Same as Answer B =$$\frac{1}{16}$$

D. $$a^{(-2)}$$--> $$\frac{1}{a^2}$$

$$\frac{1}{(\frac{1}{4})^2}$$ = $$\frac{1}{\frac{1}{16}}$$ = 16

E. $$a^2$$ = same as Answer B = $$\frac{1}{16}$$

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Re: If 0 < a < 1, which of the following is the greatest?  [#permalink]

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20 Sep 2017, 15:51
2
Bunuel wrote:
If 0 < a < 1, which of the following is the greatest?

A. $$(-2a)^{(-2)}$$

B. $$\frac{1}{a^{(-2)}}$$

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

D. $$a^{(-2)}$$

E. $$a^2$$

Since we know a is between 0 and 1, let’s let a = 1/2. Now we analyze each answer choice:

A)

[-2(1/2)]^-2 = (-1)^-2 = 1

B)

1/(1/2)^-2 = 1/(2^2) = ¼

C)

(1/(1/2))^-2 = 2^-2 = 1/4

D)

(1/2)^-2 = 2^2 = 4

E)

(1/2)^2 = 1/4

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Re: If 0 < a < 1, which of the following is the greatest?  [#permalink]

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05 Dec 2019, 20:18
Bunuel wrote:
If 0 < a < 1, which of the following is the greatest?

A. $$(-2a)^{(-2)}$$

B. $$\frac{1}{a^{(-2)}}$$

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

D. $$a^{(-2)}$$

E. $$a^2$$

We see that both choices B and D can be simplified as a^2, which is choice E; thus, we know that none of these 3 choices could be the right answer. We are left with choices A and D.

We can let a = ½. Thus, choice A becomes (-1)^(-2) = 1 and choice D becomes (½)^(-2) = 2^2 = 4. We see that choice D is has the greatest value.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
181 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: If 0 < a < 1, which of the following is the greatest?   [#permalink] 05 Dec 2019, 20:18
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