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3^7[(3^−4+3^−5)+(3^−5+3^−6)+(3^−6+3^−7)–3^−7] is what multiple of 17?
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rheam25
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3^7[(3^−4+3^−5)+(3^−5+3^−6)+(3^−6+3^−7)–3^−7] is what multiple of 17? [#permalink] New post  12 Mar 2020, 22:39
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\(3^7[\)(\(3^{−4}\)+\(3^{−5}\))+(\(3^{−5}\)+\(3^{−6}\))+(\(3^{−6}\)+\(3^{−7}\)) –\(3^{−7}\) ] is what multiple of 17?

A) 1
B) 2
C) 3
D) 4
E) 11
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BrentGMATPrepNow
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Re: 3^7[(3^−4+3^−5)+(3^−5+3^−6)+(3^−6+3^−7)–3^−7] is what multiple of 17? [#permalink] New post  13 Mar 2020, 04:36
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rheam25 wrote:
\(3^7[\)(\(3^{−4}\)+\(3^{−5}\))+(\(3^{−5}\)+\(3^{−6}\))+(\(3^{−6}\)+\(3^{−7}\)) –\(3^{−7}\) ] is what multiple of 17?

A) 1
B) 2
C) 3
D) 4
E) 11


Take: \(3^7[\)(\(3^{−4}\)+\(3^{−5}\))+(\(3^{−5}\)+\(3^{−6}\))+(\(3^{−6}\)+\(3^{−7}\)) –\(3^{−7}\) ]

Expand to get: \(3^3 + 3^2 + 3^2 + 3^1 + 3^1 + 1 - 1\)

Evaluate: \(27 + 9 + 9 + 3 + 3 + 1 - 1\)

Evaluate: \(51\)

Since \(51 = (3)(17)\), the correct answer is C

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Brent
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Shashankprasad95
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Re: 3^7[(3^−4+3^−5)+(3^−5+3^−6)+(3^−6+3^−7)–3^−7] is what multiple of 17? [#permalink] New post  29 Nov 2020, 17:38
We can simplify the equation.

3^7 [3^-4 + 2(3^-5) + 2(3^-6) ]

Note that +3^-7 and -3^-7 are cancelled in the above simplification.

Take 3^-4 as common multiple.
3^7 [3^-4 {1 + 2(3^-1) + 2(3^-2)}]

3^3 ( 1 + 2/3 + 2/9)

We get 3^3 since 3^7 (3^-4) = 3^3

3^3 (17/9)

3 (17)

Thus the multiple is 3.

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