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Math Expert V
Joined: 02 Sep 2009
Posts: 65184
2−6/3 + 2−7/6 + 2−8/12 is how many times bigger than 2^−10?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 69% (02:07) correct 31% (02:40) wrong based on 150 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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Current Student V
Joined: 24 Aug 2016
Posts: 787
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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2
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: 10664
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

Intern  B
Joined: 29 Aug 2018
Posts: 29
Re: 2−6/3 + 2−7/6 + 2−8/12 is how many times bigger than 2^−10?  [#permalink]

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

Kindly, explain how you get 21/3?
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11082
Location: United States (CA)
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

Simplifying, we have:

2^(-6) / 3 + (2^1)(2^(-8)) / 6 + (2^2)(2^(-10)) / 12

2^(-6) / 3 + 2^(-8) / 3 + 2^(-10) / 3

2^(-10) * (2^4 + 2^2 + 1) / 3

2^(-10) * 21 / 3

2^(-10) * 7

We see that the given expression is 7 times bigger than 2^(-10).

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Intern  B
Joined: 11 Sep 2019
Posts: 21
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}

Hi, I have a doubt, possibly a very stupid one,
If x=7y
isn't x 6 time more than y Re: 2−6/3 + 2−7/6 + 2−8/12 is how many times bigger than 2^−10?   [#permalink] 04 Jun 2020, 04:22

# 2−6/3 + 2−7/6 + 2−8/12 is how many times bigger than 2^−10?   