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If 4^7 + 4^8 + 4^9 + 4^10/5 is x times 4^7, what is the value of x ?

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If 4^7 + 4^8 + 4^9 + 4^10/5 is x times 4^7, what is the value of x ? [#permalink]

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New post 27 Apr 2017, 09:12
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A
B
C
D
E

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Question Stats:

78% (00:49) correct 23% (00:27) wrong based on 40 sessions

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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
[Reveal] Spoiler: OA

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Last edited by stonecold on 27 Apr 2017, 20:48, edited 1 time in total.
Edited the Question.
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Re: If 4^7 + 4^8 + 4^9 + 4^10/5 is x times 4^7, what is the value of x ? [#permalink]

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New post 27 Apr 2017, 09:33
(4^7 + 4^8 + 4^9 + 4^10)/5
=(4^7(1 + 4 + 4^2 + 4^3))/5
=(4^7(1+4+16+64))/5
=4^7(85)/5
=4^7(17) which is 17 times 4^7(Option E)
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Re: If 4^7 + 4^8 + 4^9 + 4^10/5 is x times 4^7, what is the value of x ? [#permalink]

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New post 27 Apr 2017, 09:50
(4^7 + 4^8 + 4^9 + 4^10)/5 = x * 4^7

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

=> (1+4+16+64)/5 = x

=> 85/5 = x = 17

Answer is E. 17
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Re: If 4^7 + 4^8 + 4^9 + 4^10/5 is x times 4^7, what is the value of x ? [#permalink]

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New post 27 Apr 2017, 15:46
\(4^7\)(1+4+\(4^2\)+\(4^3\))/5
\(4^7\)(1+4+16+64)/5
\(4^7\)(85)/5
\(4^7\)*17

Thus x=17
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Re: If 4^7 + 4^8 + 4^9 + 4^10/5 is x times 4^7, what is the value of x ? [#permalink]

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New post 27 Apr 2017, 20:45
Thanks for the question.

Its tagged to 700 level.
But is it 700 level?
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If 4^7 + 4^8 + 4^9 + 4^10/5 is x times 4^7, what is the value of x ? [#permalink]

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New post 27 Apr 2017, 20:51
Taking out 4^7 we get ->

\(\frac{4^7[1+4+4^2+4^3]}{5}=x*4^7\)

\(\frac{85}{5}= x\)

17=x

Hence x=17

SMASH THAT E.

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If 4^7 + 4^8 + 4^9 + 4^10/5 is x times 4^7, what is the value of x ?   [#permalink] 27 Apr 2017, 20:51
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