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17^3 + 17^4 =

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by BTGModeratorVI » Wed Apr 22, 2020 11:07 am
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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

Answer: B
Source: Official guide
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Re: 17^3 + 17^4 =

by Jay@ManhattanReview » Thu Apr 23, 2020 10:13 pm
BTGModeratorVI wrote: ↑
Wed Apr 22, 2020 11:07 am
 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

Answer: B
Source: Official guide
17^3 + 17^4 = 17^3 + 17*(17^3) = 17^3(1 + 17) = 17^3*18

The correct answer: B

Hope this helps!

-Jay
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Re: 17^3 + 17^4 =

by Brent@GMATPrepNow » Fri Apr 24, 2020 7:49 am
BTGModeratorVI wrote: ↑
Wed Apr 22, 2020 11:07 am
 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

Answer: B
Source: Official guide
Jay's solution (above) 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

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: 17^3 + 17^4 =

by Scott@TargetTestPrep » Fri Apr 24, 2020 8:17 am
BTGModeratorVI wrote: ↑
Wed Apr 22, 2020 11:07 am
 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

Answer: B
Source: Official guide
Factoring, we have:

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

Answer: B

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