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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8758
GMAT 1: 760 Q51 V42
GPA: 3.82
If A =8^10+4^10/8^4+4^11 , what is (A + 4)2?  [#permalink]

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17 Feb 2020, 00:29
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4
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Difficulty:

25% (medium)

Question Stats:

76% (02:18) correct 24% (03:12) wrong based on 51 sessions

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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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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 03 Feb 2019 Posts: 2 Re: If A =8^10+4^10/8^4+4^11 , what is (A + 4)2? [#permalink] ### Show Tags 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8758 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If A =8^10+4^10/8^4+4^11 , what is (A + 4)2? [#permalink] ### Show Tags 19 Feb 2020, 01:15 1 => $$A = \sqrt{\frac{8^{10}+4^{10}}{8^4+4^{11}}} = \sqrt{\frac{2^{30}+2^{20}}{2^{12}+2^{22}}} = \sqrt{\frac{2^{20}(2^{10}+1)}{2^{12}(2^{10}+1)}} = √2^8 = 2^4 = 16$$ Then, $$(A + 4)^2 = (16 + 4)^2 = 20^2 = 400.$$ Therefore, C is the answer. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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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