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# Which of the following is closest to

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4715
GPA: 3.82
Which of the following is closest to [#permalink]

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20 Dec 2017, 01:08
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62% (00:53) correct 38% (00:53) wrong based on 55 sessions

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[GMAT math practice question]
Which of the following is closest to $$\frac{(1+10^{26})}{(5^4+10^{10})}$$?

A. 10^{15}
B. 10^{16}
C. 10^{17}
D. 10^{18}
E. 10^{19}
[Reveal] Spoiler: OA

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Joined: 22 May 2016
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Which of the following is closest to [#permalink]

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20 Dec 2017, 07:56
MathRevolution wrote:
[GMAT math practice question]
Which of the following is closest to $$\frac{(1+10^{26})}{(5^4+10^{10})}$$?

A. 10^{15}
B. 10^{16}
C. 10^{17}
D. 10^{18}
E. 10^{19}

Ignore $$1$$ and $$5^4$$. They are much too small to matter compared to $$10^{26}$$ and $$10^{10}$$

Take an example of much "closer" numbers, where the "extra" amount matters more:
$$\frac{10^6}{10^4 + 50}= \frac{10^6}{10,050}\approx{99.5}$$

$$\frac{10^6}{10^4}= 100 = 10^2$$

$$99.5$$ is much closer to $$10^2$$ than to $$10^1$$

Hence consider only the powers of 10: $$10^{(26-10)} = 10^{16}$$

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Formerly genxer123

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4715
GPA: 3.82
Re: Which of the following is closest to [#permalink]

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22 Dec 2017, 05:47
=>

$$\frac{(1+10^{26})}{(5^4+10^{10})}$$
$$≒ \frac{10^{26}}{10^{10}} = 10^{16}$$

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Intern
Joined: 20 Dec 2017
Posts: 8
Re: Which of the following is closest to [#permalink]

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22 Dec 2017, 06:12
Re: Which of the following is closest to   [#permalink] 22 Dec 2017, 06:12
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