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# If 1+2+2^2+... +2^n=2^{n+1}-1, what is the largest prime factor of 1+2

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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If 1+2+2^2+... +2^n=2^{n+1}-1, what is the largest prime factor of 1+2  [#permalink]

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27 Nov 2018, 02:40
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Difficulty:

35% (medium)

Question Stats:

63% (01:17) correct 38% (01:45) wrong based on 46 sessions

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[Math Revolution GMAT math practice question]

If $$1+2+2^2+... +2^n=2^{n+1}-1$$, what is the largest prime factor of $$1+2+2^2+... +2^7$$?

$$A. 3$$
$$B. 5$$
$$C. 13$$
$$D. 17$$
$$E. 19$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 18 Jul 2018 Posts: 897 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) Re: If 1+2+2^2+... +2^n=2^{n+1}-1, what is the largest prime factor of 1+2 [#permalink] ### Show Tags 27 Nov 2018, 02:58 1 $$1+2+2^2+....+2^7$$ = 1+ GP series Sum of GP series = $$\frac{a(r^n-1)}{r-1}$$ a = first term = 2. r = common ratio = 2. Sum = $$\frac{2(2^7-1)}{2-1}$$ = 254. Total = 254+1 = 255. Prime factorizing 255 gives 3*5*17. Largest prime is 17. D is the answer. _________________ Press +1 Kudo If my post helps! Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7343 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If 1+2+2^2+... +2^n=2^{n+1}-1, what is the largest prime factor of 1+2 [#permalink] ### Show Tags 29 Nov 2018, 02:46 1 => $$1+2+2^2+... +2^7 = 2^8 – 1 = (2^4+1)(2^4-1) = (2^4+1)(2^2+1)(2^2-1) = (2^4+1)(2^2+1)(2+1)(2-1) = 17*5*3.$$ $$17$$ is the largest prime factor of $$1+2+2^2+... +2^7.$$ Therefore, D is the answer. Answer: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: If 1+2+2^2+... +2^n=2^{n+1}-1, what is the largest prime factor of 1+2   [#permalink] 29 Nov 2018, 02:46
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