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M07-32

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M07-32 [#permalink]

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New post 16 Sep 2014, 00:35
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\((\frac{1}{2})^2 + (\frac{1}{4})^{-2} + (\frac{1}{8})^{\frac{2}{3}} + (\frac{1}{4})^{\frac{1}{2}} =\) ?

A. \(20(\frac{3}{4})\)
B. \(17\)
C. \(9(\frac{1}{2})\)
D. \(6\)
E. \(4(\frac{3}{4})\)
[Reveal] Spoiler: OA

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New post 16 Sep 2014, 00:36
Official Solution:

\((\frac{1}{2})^2 + (\frac{1}{4})^{-2} + (\frac{1}{8})^{\frac{2}{3}} + (\frac{1}{4})^{\frac{1}{2}} =\) ?

A. \(20(\frac{3}{4})\)
B. \(17\)
C. \(9(\frac{1}{2})\)
D. \(6\)
E. \(4(\frac{3}{4})\)


Simplify the expression as follows.
\(\frac{1}{2^2} = \frac{1}{4}\)
\((\frac{1}{4})^{-2} = 4^2 = 16\)

A number taken to a negative power equals its reciprocal taken to the same power but with a positive sign.
\(\frac{1}{8^{\frac{2}{3}}} = \frac{1}{\sqrt[3]{8^2}} = \frac{1}{4}\)

As a general rule,
\((\frac{a}{b})^{\frac{n}{m}} = \sqrt{(\frac{a}{b})^n}\)
\(\frac{1}{4}^{\frac{1}{2}} = \frac{1}{2}\)

The sum is:
\(\frac{1}{4} + 16 + \frac{1}{4} + \frac{1}{2} = 17\)


Answer: B
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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M07-32 [#permalink]

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New post 28 Dec 2015, 23:21
Bunuel wrote:
Official Solution:

\((\frac{1}{2})^2 + (\frac{1}{4})^{-2} + (\frac{1}{8})^{\frac{2}{3}} + (\frac{1}{4})^{\frac{1}{2}} =\) ?

A. \(20(\frac{3}{4})\)
B. \(17\)
C. \(9(\frac{1}{2})\)
D. \(6\)
E. \(4(\frac{3}{4})\)


Simplify the expression as follows.
\(\frac{1}{2^2} = \frac{1}{4}\)
\((\frac{1}{4})^{-2} = 4^2 = 16\)

A number taken to a negative power equals its reciprocal taken to the same power but with a positive sign.
\(\frac{1}{8^{\frac{2}{3}}} = \frac{1}{\sqrt[3]{8^2}} = \frac{1}{4}\)

As a general rule,
\((\frac{a}{b})^{\frac{n}{m}} = \sqrt{(\frac{a}{b})^n}\)
\(\frac{1}{4}^{\frac{1}{2}} = \frac{1}{2}\)

The sum is:
\(\frac{1}{4} + 16 + \frac{1}{4} + \frac{1}{2} = 17\)

Answer: B


Hello Bunuel,

If i am not wrong, you have assumed as m=2 at this case.

Pls clarify..................

And also if you could share some similar question for practice, it would be great 8-)

Thanks,
Arun

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Re: M07-32 [#permalink]

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New post 25 Sep 2017, 08:40
Hi Bunuel, I have the same doubt as ArunpriyanJ

Appreciate if you can explain a bit further why we assume m=2 in your explanation.

Thanks!

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Re: M07-32   [#permalink] 25 Sep 2017, 08:40
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