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Which of the following is closest to

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Math Revolution GMAT Instructor
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Which of the following is closest to [#permalink]

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New post 20 Dec 2017, 02:08
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Question Stats:

59% (01:11) correct 41% (01:21) wrong based on 90 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}

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Which of the following is closest to [#permalink]

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New post 20 Dec 2017, 08:56
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: \(10^{(26-10)} = 10^{16}\)

Answer B
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Expert Post
Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
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Re: Which of the following is closest to [#permalink]

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New post 22 Dec 2017, 06:47
=>

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

Therefore, the answer is B.

Answer: B
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Re: Which of the following is closest to [#permalink]

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New post 22 Dec 2017, 07:12
Oh, looks like I have idea about the right answer.. Could you please help me with this?
Manager
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Re: Which of the following is closest to [#permalink]

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New post 01 Feb 2018, 10:16
I understand ignoring 1 in the numerator is understood but isnt 5^4 = 625 isnt too big at numerator level

eg: 10^4 = 10000/625 = 16 ..that reduces almost 10^4 from the answers others have given which is 10^16, thus I thought A is right answer.

Bunuel, could please explain
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Re: Which of the following is closest to [#permalink]

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New post 01 Feb 2018, 12:05
MathRevolution wrote:
=>

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

Therefore, the answer is B.

Answer: B



how can I bring \(1^1\) and \(5^4\) to the same base ? :?
Re: Which of the following is closest to   [#permalink] 01 Feb 2018, 12:05
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