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OG Negative Exponents Q

This topic has 4 expert replies and 0 member replies
AbeNeedsAnswers Master | Next Rank: 500 Posts Default Avatar
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OG Negative Exponents Q

Post Wed Jul 19, 2017 10:04 pm
The value of [2^(-14) + 2^(-15) + 2^(-16) + 2^(-17)]/ 5 is how many times the value of 2^(-17)?

A. 3/2
B. 5/2
C. 3
D. 4
E. 5

C

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Post Tue Jul 25, 2017 11:04 am
AbeNeedsAnswers wrote:
The value of [2^(-14) + 2^(-15) + 2^(-16) + 2^(-17)]/ 5 is how many times the value of 2^(-17)?

A. 3/2
B. 5/2
C. 3
D. 4
E. 5
We can create the following equation in which k is an integer:

[2^(-14) + 2^(-15) + 2^(-16) + 2^(-17)]/5 = (k)(2^-17)

[2^(-14) + 2^(-15) + 2^(-16) + 2^(-17)] = (k)(2^-17)(5)

We pull out the common factor 2^-17 from each term on the left side of the equation:

2^-17[2^3 + 2^2 + 2^1 + 1] = (k)(2^-17)(5)

We eliminate 2^-17 from each side of the equation:

(8 + 4 + 2 + 1) = 5k

15 = 5k

3 = k

Answer: C

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Post Mon Jul 24, 2017 11:20 am
AbeNeedsAnswers wrote:
The value of [2^(-14) + 2^(-15) + 2^(-16) + 2^(-17)]/ 5 is how many times the value of 2^(-17)?

A. 3/2
B. 5/2
C. 3
D. 4
E. 5

C
Here's my solution

ttps://postimg.org/image/4gg1xoq97/" target="_blank">

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Matt@VeritasPrep GMAT Instructor
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Post Sun Jul 23, 2017 5:19 pm
Let's rephrase the question first. We're asked to solve for x in the following:

(2⁻¹⁴ + 2⁻¹⁵ + 2⁻¹⁶ + 2⁻¹⁷)/5 = x * 2⁻¹⁷

Let's multiply both sides by 5:

(2⁻¹⁴ + 2⁻¹⁵ + 2⁻¹⁶ + 2⁻¹⁷) = 5x * 2⁻¹⁷

Then divide both sides by 2⁻¹⁷:

2³ + 2² + 2 + 1 = 5x

which simplifies to

3 = x

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Post Thu Jul 20, 2017 12:16 am
AbeNeedsAnswers wrote:
The value of [2^(-14) + 2^(-15) + 2^(-16) + 2^(-17)]/ 5 is how many times the value of 2^(-17)?

A. 3/2
B. 5/2
C. 3
D. 4
E. 5

C
Say the value of [2^(-14) + 2^(-15) + 2^(-16) + 2^(-17)]/ 5 is x times the value of 2^(-17).

We then need to get the value of x.

=> [2^(-14) + 2^(-15) + 2^(-16) + 2^(-17)] / 5 = 2^(-17)*x

Taking 2^(-17) common from the RHS. We get,

2^(-17)[[2^(3) + 2^(2) + 2^(1) + 1] / 5] = 2^(-17)*x

=> [2^(3) + 2^(2) + 2^(1) + 1] / 5 = x; 2^(-17) gets cancelled

= [8 + 4 + 2 + 1] /5 = x

= [15] /5 = x

x = 3.

The correct answer: C

Hope this helps!

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