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If A =8^10+4^10/8^4+4^11 , what is (A + 4)2?

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If A =8^10+4^10/8^4+4^11 , what is (A + 4)2?  [#permalink]

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New post 17 Feb 2020, 00:29
1
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

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[GMAT math practice question]

If \(A =\sqrt{\frac{8^{10}+4^{10}}{8^4+4^{11}}}\) , what is \((A + 4)^2\)?

A. \(20\)

B. \(225\)

C. \(400\)

D. \(500\)

E. \(900\)

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Re: If A =8^10+4^10/8^4+4^11 , what is (A + 4)2?  [#permalink]

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New post 17 Feb 2020, 00:48
Reducing the fraction to power of 2 we get:

\sqrt{(2^20(2^10+1)/2^12(1+2^10))}

Further the equation gives \sqrt{2^8}

which equals 2^4 which is 16

and hence (A+4)^2 gives 400
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Re: If A =8^10+4^10/8^4+4^11 , what is (A + 4)2?  [#permalink]

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New post 19 Feb 2020, 01:15
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\(A = \sqrt{\frac{8^{10}+4^{10}}{8^4+4^{11}}} = \sqrt{\frac{2^{30}+2^{20}}{2^{12}+2^{22}}} = \sqrt{\frac{2^{20}(2^{10}+1)}{2^{12}(2^{10}+1)}} = √2^8 = 2^4 = 16\)

Then, \((A + 4)^2 = (16 + 4)^2 = 20^2 = 400.\)

Therefore, C is the answer.
Answer: C
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Re: If A =8^10+4^10/8^4+4^11 , what is (A + 4)2?   [#permalink] 19 Feb 2020, 01:15
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