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Math Expert V
Joined: 02 Sep 2009
Posts: 58445
2−6/3 + 2−7/6 + 2−8/12 is how many times bigger than 2^−10?  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 73% (01:59) correct 27% (02:44) wrong based on 67 sessions

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$$\frac{2^{−6}}{3} + \frac{2^{−7}}{6} + \frac{2^{−8}}{12}$$ is how many times bigger than $$2^{−10}$$?

A. 29/21

B. 3

C. 31/6

D. 7

E. 28/3

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RC Moderator V
Joined: 24 Aug 2016
Posts: 789
GMAT 1: 540 Q49 V16 GMAT 2: 680 Q49 V33 Re: 2−6/3 + 2−7/6 + 2−8/12 is how many times bigger than 2^−10?  [#permalink]

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Bunuel wrote:
$$\frac{2^{−6}}{3} + \frac{2^{−7}}{6} + \frac{2^{−8}}{12}$$ is how many times bigger than $$2^{−10}$$?

A. 29/21

B. 3

C. 31/6

D. 7

E. 28/3

$$\frac{2^{−6}}{3} + \frac{2^{−7}}{6} + \frac{2^{−8}}{12}$$
= $$\frac{1}{3*2^{6}} + \frac{1}{2*3*2^{7}} + \frac{1}{2^{2}*3*2^{8}}$$
= $$\frac{2^{4}+2^{2}+1}{2^{2}*3*2^{8}}$$
= $$\frac{21}{2^{2}*3*2^{8}}$$
= $$\frac{7}{2^{2}*2^{8}}$$
= $$7*2^{-10}$$

Ans D
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Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: 2−6/3 + 2−7/6 + 2−8/12 is how many times bigger than 2^−10?  [#permalink]

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Bunuel wrote:
$$\frac{2^{−6}}{3} + \frac{2^{−7}}{6} + \frac{2^{−8}}{12}$$ is how many times bigger than $$2^{−10}$$?

A. 29/21

B. 3

C. 31/6

D. 7

E. 28/3

$$\frac{2^{−6}}{3} + \frac{2^{−7}}{6} + \frac{2^{−8}}{12}$$

$$2^{-8} * (\frac{4}{3} + \frac{2}{6} + \frac{1}{12}$$

$$2^{-8} * \frac{21}{12}$$

We know that $$2^{-10} = \frac{2^{-8}}{4}$$

So our expression is 21/3 (= 7) times more than 2^{-10}

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Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Re: 2−6/3 + 2−7/6 + 2−8/12 is how many times bigger than 2^−10?   [#permalink] 25 Oct 2018, 22:41
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