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(3^3+3^4+3^5+3^6)^2=?

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(3^3+3^4+3^5+3^6)^2=? [#permalink]

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[GMAT math practice question]

\((3^3+3^4+3^5+3^6)^2=?\)

\(A. 2^43^65^2\)
\(B. 2^63^45^2\)
\(C. 2^83^65^2\)
\(D. 2^63^85^2\)
\(E. 2^63^65^2\)
[Reveal] Spoiler: OA

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(3^3+3^4+3^5+3^6)^2=? [#permalink]

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New post 02 Nov 2017, 01:32
\((3^3+3^4+3^5+3^6)^2\) =\((3^3(1+3)+3^5(1+3))^2\)

=\(((3^3 + 3^5)(1+3))^2\) =\(((3^3)(1 + 3^2)(1+3))^2\)

=\(((3^3)(10)(4))^2\) =\(((3^3)(5)(2^3))^2\) =\((3^6)(5^2)(2^6)\) (Option E)
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Re: (3^3+3^4+3^5+3^6)^2=? [#permalink]

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New post 05 Nov 2017, 07:26
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MathRevolution wrote:
[GMAT math practice question]

\((3^3+3^4+3^5+3^6)^2=?\)

\(A. 2^43^65^2\)
\(B. 2^63^45^2\)
\(C. 2^83^65^2\)
\(D. 2^63^85^2\)
\(E. 2^63^65^2\)


We can simplify the given expression by factoring out 3^3:

[3^3(1 + 3^1 + 3^2 + 3^3)]^2

[3^3(1 + 3 + 9 + 27)]^2

[3^3(40)]^2

3^6 x 40^2 = 3^6 x (5^1 x 2^3)^2 = 2^6 x 3^6 x 5^2

Answer: E
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Re: (3^3+3^4+3^5+3^6)^2=? [#permalink]

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New post 05 Nov 2017, 17:24
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\((3^3+3^4+3^5+3^6)^2= (3^3(3^0+3^1+3^2+3^3))^2=3^6(1+3+9+27)^2=3^640^2=3^62^65^2\)


Therefore, the answer is E.
Answer: E
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Re: (3^3+3^4+3^5+3^6)^2=?   [#permalink] 05 Nov 2017, 17:24
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