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(2^5+2^6+2^7+2^8)^2=?

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Math Revolution GMAT Instructor
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(2^5+2^6+2^7+2^8)^2=?  [#permalink]

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New post 10 May 2018, 07:00
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

70% (01:12) correct 30% (01:35) wrong based on 122 sessions

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[GMAT math practice question]

\((2^5+2^6+2^7+2^8)^2=?\)

\(A. 2^83^25^2\)
\(B. 2^{10}3^45^4\)
\(C. 2^{10}+2^{12}+2^{14}+2^{16}\)
\(D. 2^{25}+2^{36}+2^{49}+2^{64}\)
\(E. 2^{10}3^25^2\)

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Re: (2^5+2^6+2^7+2^8)^2=?  [#permalink]

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New post 10 May 2018, 07:32
MathRevolution wrote:
[GMAT math practice question]

\((2^5+2^6+2^7+2^8)^2=?\)

\(A. 2^83^25^2\)
\(B. 2^{10}3^45^4\)
\(C. 2^{10}+2^{12}+2^{14}+2^{16}\)
\(D. 2^{25}+2^{36}+2^{49}+2^{64}\)
\(E. 2^{10}3^25^2\)



\((2^5+2^6+2^7+2^8)^2\)
=\(2^{10}*(1+2+2^2+2^3)^2\)
=\(2^{10}*(1+2+4+8)^2\)
=\(2^{10}*15^2\)
=\(2^{10}3^25^2\)..... Hence I would go for option E.
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Re: (2^5+2^6+2^7+2^8)^2=?  [#permalink]

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New post 13 May 2018, 17:43
1
=>

\((2^5+2^6+2^7+2^8)^2\)
\(= (2^5 ( 2^0 + 2^1 + 2^2 + 2^3 ))^2\)
\(= (2^5 ( 1 + 2 + 4 + 8 ))^2\)
\(= (2^5 (15))^2\)
\(= (2^5 (3*5))^2\)
\(= 2^{10}*3^2*5^2\)

Therefore, E is the answer.
Answer : E
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Re: (2^5+2^6+2^7+2^8)^2=?  [#permalink]

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New post 01 Sep 2018, 16:15
MathRevolution whats wrong in option C?
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Re: (2^5+2^6+2^7+2^8)^2=?  [#permalink]

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New post 10 Sep 2018, 04:47
1
parthos wrote:
MathRevolution whats wrong in option C?


\((2^5+2^6+2^7+2^8)^2\) = \((2^5+2^6+2^7+2^8)*(2^5+2^6+2^7+2^8)\)

This is not the same as squaring each term in the equation.

Think of it with simple numbers \((3+4)^2\)=7*7=49, this is not the same as \(3^2+4^2\)= 9+16=25

Maybe take a look at these links here: https://gmatclub.com/forum/math-algebra-101576.html
https://gmatclub.com/forum/ultimate-gma ... 44512.html
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Re: (2^5+2^6+2^7+2^8)^2=?  [#permalink]

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New post 11 Sep 2018, 07:25
T1101 wrote:
parthos wrote:
MathRevolution whats wrong in option C?


\((2^5+2^6+2^7+2^8)^2\) = \((2^5+2^6+2^7+2^8)*(2^5+2^6+2^7+2^8)\)

This is not the same as squaring each term in the equation.

Think of it with simple numbers \((3+4)^2\)=7*7=49, this is not the same as \(3^2+4^2\)= 9+16=25

Maybe take a look at these links here: https://gmatclub.com/forum/math-algebra-101576.html
https://gmatclub.com/forum/ultimate-gma ... 44512.html


Thanks !!
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Consider KUDOS if my post helped !!

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Re: (2^5+2^6+2^7+2^8)^2=?  [#permalink]

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New post 14 Sep 2018, 16:46
1
MathRevolution wrote:
[GMAT math practice question]

\((2^5+2^6+2^7+2^8)^2=?\)

\(A. 2^83^25^2\)
\(B. 2^{10}3^45^4\)
\(C. 2^{10}+2^{12}+2^{14}+2^{16}\)
\(D. 2^{25}+2^{36}+2^{49}+2^{64}\)
\(E. 2^{10}3^25^2\)


Factoring out the common 2^5 from the four terms, we have:

[2^5(1 + 2^1 + 2^2 + 2^3)]^2

[2^5(15)]^2

(2^5 x 3^1 x 5^1)^2

2^10 x 3^2 x 5^2

Answer: E
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Re: (2^5+2^6+2^7+2^8)^2=? &nbs [#permalink] 14 Sep 2018, 16:46
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