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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7343
GMAT 1: 760 Q51 V42 GPA: 3.82
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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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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Director  D
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]

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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.
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Math Revolution GMAT Instructor V
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]

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

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