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Math Expert V
Joined: 02 Sep 2009
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Question Stats: 86% (00:30) correct 14% (00:47) wrong based on 1009 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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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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

APPROACH #1:
Take: $$17^3 + 17^4$$
Factor: $$17^3(1+17)$$
Evaluate: $$17^3 \times 18$$

APPROACH #2 (for fun)
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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If you enjoy my solutions, you'll love my GMAT prep course. Originally posted by BrentGMATPrepNow on 02 Dec 2016, 13:38.
Last edited by BrentGMATPrepNow on 27 May 2020, 11:55, edited 1 time in total.
##### General Discussion
Math Expert V
Joined: 02 Sep 2009
Posts: 65829
Re: 17^3 + 17^4 =  [#permalink]

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2
1
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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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

$$17^3 + 17^4$$

Or, $$17^3( 1 + 17)$$

Or, $$17^3*18$$, thus answer will be (B)
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Re: 17^3 + 17^4 =  [#permalink]

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WRT Question
17^3+17^4
= 17^3(common) [1+17]
=17^3*18
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
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Re: 17^3 + 17^4 =  [#permalink]

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Bunuel wrote:
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

17^3 + 17^4 = 17^3(1 + 17) = 17^3 x 18

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Re: 17^3 + 17^4 =  [#permalink]

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Bunuel wrote:
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

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

Hi Bunuel, how do you call this rule when from this $$17^3 + 17^4$$ you get this $$17^3(1+17)$$ ? please explain in two or three words Math Expert V
Joined: 02 Sep 2009
Posts: 65829
Re: 17^3 + 17^4 =  [#permalink]

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1
dave13 wrote:
Bunuel wrote:
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

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

Hi Bunuel, how do you call this rule when from this $$17^3 + 17^4$$ you get this $$17^3(1+17)$$ ? please explain in two or three words We are factoring out common term 17^3 from 17^3 + 17*17^3 to get 17^3(1+17).
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Re: 17^3 + 17^4 =  [#permalink]

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Bunuel wrote:
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

17^3 + 17^4 = 17^3 (1+ 17) = 17^3 (18)

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Posts: 1675
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Re: 17^3 + 17^4 =  [#permalink]

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Bunuel wrote:
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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

17^3 + 17^4

Or, 17^3(1 + 17)

17^3 * 18

(B)
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Joined: 11 Sep 2015
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GMAT 1: 770 Q49 V46
Re: 17^3 + 17^4 =  [#permalink]

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Top Contributor
Bunuel wrote:
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

$$17^3 + 17^4$$ has the same format as $$x^3 + x^4$$, which we can factor as follows: $$x^3(1 + x)$$
The same applies to the given expression.
$$17^3 + 17^4=17^3(1 + 17)$$
$$=(17^3)(18)$$

Cheers,
Brent
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If you enjoy my solutions, you'll love my GMAT prep course.  Re: 17^3 + 17^4 =   [#permalink] 17 Jun 2019, 12:01

# 17^3 + 17^4 =  