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Which of the following is the closest to 11^59^5 – 2(10^5)?

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Which of the following is the closest to 11^59^5 – 2(10^5)?  [#permalink]

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New post 05 Dec 2017, 02:02
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Difficulty:

  55% (hard)

Question Stats:

55% (01:31) correct 45% (01:55) wrong based on 119 sessions

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[GMAT math practice question]

Which of the following is the closest to \(11^59^5 – 2(10^5)\)?

A. \(10^2\)
B. \(10^7\)
C. \(10^8\)
D. \(10^9\)
E. \(10^{10}\)

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Which of the following is the closest to 11^59^5 – 2(10^5)?  [#permalink]

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New post 05 Dec 2017, 05:52
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MathRevolution wrote:
[GMAT math practice question]

Which of the following is the closest to \(11^59^5 – 2(10^5)\)?

A. \(10^2\)
B. \(10^7\)
C. \(10^8\)
D. \(10^9\)
E. \(10^{10}\)



\(11^59^5 – 2(10^5) = 99^5-2*10^5\)

Now \(2*10^5\) is very small quantity in front of \(99^5\),( which is nearly equal to 100^5 = 10^{10})....
\(\frac{2*10^5}{10^{10}} = \frac{2}{10^5}=\frac{1}{50000}\),
Hence \(2*10^5\) is \(\frac{1}{50000}\) of \(100^5\), so can be neglected ..

hence answer is \(10^{10}\)

E
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Which of the following is the closest to 11^59^5 – 2(10^5)?  [#permalink]

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New post 05 Dec 2017, 12:14
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MathRevolution wrote:
[GMAT math practice question]

Which of the following is the closest to \(11^59^5 – 2(10^5)\)?

A. \(10^2\)
B. \(10^7\)
C. \(10^8\)
D. \(10^9\)
E. \(10^{10}\)


As we have to find approximate answer so we can slightly reduce or increase the number to arrive at the closest value.

\(11^59^5 – 2(10^5)\), here I'll reduce \(11\) by \(1\) and increase \(9\) by \(1\), so in totality effect should balance out

\(11^59^5 – 2(10^5)\) \(=10^5*10^5 – 2*10^5\)

\(=>10^5(10^5 – 2)\). as \(10^5\) is far greater than \(2\) so \(10^5-2=10^5\) (approximate value)

\(=>10^5*10^5=10^{10}\)

Option E
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Re: Which of the following is the closest to 11^59^5 – 2(10^5)?  [#permalink]

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New post 07 Dec 2017, 01:02
=>

\(11^59^5 – 2(10^5)\)
\(≒ 10^510^5 – 2(10^5)\)
\(= 10^{10} – 2(10^5)\)
\(≒ 10^{10}\)

Therefore, the answer is E.

Answer: E
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Re: Which of the following is the closest to 11^59^5 – 2(10^5)?  [#permalink]

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Re: Which of the following is the closest to 11^59^5 – 2(10^5)?   [#permalink] 06 Mar 2019, 19:47
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