17^3 + 17^4 = : GMAT Problem Solving (PS)
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# 17^3 + 17^4 =

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21 Feb 2014, 00:06
Expert's post
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Difficulty:

5% (low)

Question Stats:

85% (01:21) correct 15% (00:49) wrong based on 413 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

17^3 + 17^4 =

(A) 17^7
(B) 17^3*18
(C) 17^6*18
(D) 2*17^3 + 17
(E) 2*17^3 - 17

Problem Solving
Question: 108
Category: Arithmetic Exponents
Page: 75
Difficulty: 550

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Re: 17^3 + 17^4 = [#permalink]

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21 Feb 2014, 00:06
Expert's post
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SOLUTION

17^3 + 17^4 =

(A) 17^7
(B) 17^3*18
(C) 17^6*18
(D) 2*17^3 + 17
(E) 2*17^3 - 17

$$17^3 + 17^4 =17^3(1+17)=17^3*18$$.

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Re: 17^3 + 17^4 = [#permalink]

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21 Feb 2014, 00:57
Taking 17^3 common:-
17^3 + 17^4 =17^3(1+17)=17^3*18
Option (B)
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Re: 17^3 + 17^4 = [#permalink]

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21 Feb 2014, 23:10
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Factor out 17^3
17^3(1+17^1)
17^3(18)

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Re: 17^3 + 17^4 = [#permalink]

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22 Feb 2014, 05:30
SOLUTION

17^3 + 17^4 =

(A) 17^7
(B) 17^3*18
(C) 17^6*18
(D) 2*17^3 + 17
(E) 2*17^3 - 17

$$17^3 + 17^4 =17^3(1+17)=17^3*18$$.

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Re: 17^3 + 17^4 = [#permalink]

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02 Dec 2016, 13:38
Top Contributor
17^3 + 17^4 =

(A) 17^7
(B) 17^3 x 18
(C) 17^6 x 18
(D) 2 x 17^3 + 17
(E) 2 x 17^3 - 17

Bunuel's solution is great.
Just for kicks though, I thought I'd show that we can factor 17^3 + 17^4 a different way and STILL arrive at the correct answer.

17^3 + 17^4 = 17^4[17^(-1) + 1]
= 17^4(1/17 + 1)
= 17^4(1/17 + 17/17)
= 17^4(18/17)
= 17^3 x 18

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Re: 17^3 + 17^4 = [#permalink]

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07 Dec 2016, 15:57
Factor 17^3
17^3(1+17^1)
17^3(18)

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Re: 17^3 + 17^4 = [#permalink]

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08 Dec 2016, 09:47
Bunuel wrote:
17^3 + 17^4 =

(A) 17^7
(B) 17^3*18
(C) 17^6*18
(D) 2*17^3 + 17
(E) 2*17^3 - 17

$$17^3 + 17^4$$

$$= 17^3 ( 1 + 17 )$$

$$= 17^3 *18$$

Hence, answer will be (B) $$17^3 *18$$

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Re: 17^3 + 17^4 =   [#permalink] 08 Dec 2016, 09:47
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