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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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Re: 3^7[(3^4+3^5)+(3^5+3^6)+(3^6+3^7)3^7] is what multiple of 17? [#permalink]
BrentGMATPrepNow wrote:
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

Cheers,
Brent

hi
In this question can you please explain this expansion? "Expand to get: $$3^3 + 3^2 + 3^2 + 3^1 + 3^1 + 1 - 1$$". I didn't understand it
Re: 3^7[(3^4+3^5)+(3^5+3^6)+(3^6+3^7)3^7] is what multiple of 17? [#permalink]
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