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If \(\frac{4^7+4^8+4^9+4^{10}}{5}\) is \(x\) times 4^7, what

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by M7MBA » Tue Apr 30, 2019 1:04 am
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If \(\frac{4^7+4^8+4^9+4^{10}}{5}\) is \(x\) times \(4^7\), what is the value of \(x?\)

A. 1/5
B. 4/5
C. 5
D. 13
E. 17

[spoiler]OA=E[/spoiler]

Source: Princeton Review
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by Ian Stewart » Tue Apr 30, 2019 3:45 am
Just factor out 4^7 from the sum in the numerator:

(4^7 + 4^8 + 4^9 + 4^10)/5 = x*4^7
4^7(1 + 4 + 4^2 + 4^3)/5 = x*4^7

and now if we divide by 4^7 on both sides, we have

1 + 4 + 4^2 + 4^3 = 5x
85 = 5x
17 = x
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by Scott@TargetTestPrep » Thu May 02, 2019 4:18 pm
M7MBA wrote:If \(\frac{4^7+4^8+4^9+4^{10}}{5}\) is \(x\) times \(4^7\), what is the value of \(x?\)

A. 1/5
B. 4/5
C. 5
D. 13
E. 17

[spoiler]OA=E[/spoiler]

Source: Princeton Review
The common factor in the numerator is 4^7. We can simplify the equation and solve for x:

4^7(1 + 4^1 + 4^2 + 4^3) = 5(x)(4^7)

1 + 4^1 + 4^2 + 4^3 = 5x

1 + 4 + 16 + 64 = 5x

85 = 5x

17 = x

Answer: E

Scott Woodbury-Stewart
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by Scott@TargetTestPrep » Thu May 02, 2019 4:18 pm
M7MBA wrote:If \(\frac{4^7+4^8+4^9+4^{10}}{5}\) is \(x\) times \(4^7\), what is the value of \(x?\)

A. 1/5
B. 4/5
C. 5
D. 13
E. 17

[spoiler]OA=E[/spoiler]

Source: Princeton Review
The common factor in the numerator is 4^7. We can simplify the equation and solve for x:

4^7(1 + 4^1 + 4^2 + 4^3) = 5(x)(4^7)

1 + 4^1 + 4^2 + 4^3 = 5x

1 + 4 + 16 + 64 = 5x

85 = 5x

17 = x

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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