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Of the following, which is greatest?

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Of the following, which is greatest?  [#permalink]

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New post 05 Jul 2018, 01:48
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A
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C
D
E

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Of the following, which is greatest?


A. \((\frac{1}{5})^{(−2)}\)

B. \((\frac{1}{3})^{(−2)}\)

C. \(3^{(−2)}\)

D. \(5^{(−2)}\)

E. \(2^3\)
Spoiler: OA

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Re: Of the following, which is greatest?  [#permalink]

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New post 05 Jul 2018, 02:13
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Bunuel wrote:
Of the following, which is greatest?


A. \((\frac{1}{5})^{(−2)}\)

B. \((\frac{1}{3})^{(−2)}\)

C. \(3^{(−2)}\)

D. \(5^{(−2)}\)

E. \(2^3\)



Hi...

When there is a negative power, the numerator and denominator interchange and power becomes positive..




A. \((\frac{1}{5})^{(−2)}=5^3=25\)

B. \((\frac{1}{3})^{(−2)}=3^2=9\)

C. \(3^{(−2)}=(1/3)^2=1/9\)

D. \(5^{(−2)}=(1/5)^2=1/25\)

E. \(2^3=8\)

Ans A
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
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Re: Of the following, which is greatest?  [#permalink]

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New post 05 Jul 2018, 02:33
Ans: A
C and D are out of the picture because they will give fraction of 1/n; so it can not be the greatest.
Out of A=25, B=9 and E=8, A is the highest for A= 25.

Bunuel wrote:
Of the following, which is greatest?

A. \((\frac{1}{5})^{(−2)}\)

B. \((\frac{1}{3})^{(−2)}\)

C. \(3^{(−2)}\)

D. \(5^{(−2)}\)

E. \(2^3\)

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Of the following, which is greatest?  [#permalink]

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New post 05 Jul 2018, 15:39
Bunuel wrote:
Of the following, which is greatest?


A. \((\frac{1}{5})^{(−2)}\)

B. \((\frac{1}{3})^{(−2)}\)

C. \(3^{(−2)}\)

D. \(5^{(−2)}\)

E. \(2^3\)




Option A :

\((\frac{1}{5})^{(−2)}\)

= 1 / (1/ \(5 ^2\))

= 25.

Thus the best answer is A.
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Re: Of the following, which is greatest?  [#permalink]

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New post 06 Jul 2018, 02:15

Solution


To find:
    • Which is greatest among the given options?

Approach and Working:
    • \((1/5)^{-2}\) = \((5^{-1})^{-2}\)= \(5^2\) = 25
    • Similarly, \((1/3)^{-2} = 3^2\) = 9
    • \(3^{-2} = 1/3^2\) = 1/9
    • Similarly, \(5^{-2}\) = 1/25
    • \(2^3\) = 8

Hence, the correct answer is option A.

Answer: A
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Re: Of the following, which is greatest?  [#permalink]

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New post 09 Jul 2018, 19:56
Bunuel wrote:
Of the following, which is greatest?


A. \((\frac{1}{5})^{(−2)}\)

B. \((\frac{1}{3})^{(−2)}\)

C. \(3^{(−2)}\)

D. \(5^{(−2)}\)

E. \(2^3\)


Simplifying answers A through E, we have:

25, 9, 1/9, 1/25, 8

So, the greatest is A.

Answer: A
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Re: Of the following, which is greatest?   [#permalink] 09 Jul 2018, 19:56
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