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Which of the following is the closest to 11*10^10–4*10^4?

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Which of the following is the closest to 11*10^10–4*10^4? [#permalink]

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New post 01 Sep 2017, 10:08
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Which of the following is the closest to \(11*10^{10}–4*10^4\)?

A. \(10^2\)
B. \(10^7\)
C. \(10^8\)
D. \(10^9\)
E. \(10^{11}\)
[Reveal] Spoiler: OA

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Which of the following is the closest to 11*10^10–4*10^4? [#permalink]

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New post 01 Sep 2017, 11:27
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MathRevolution wrote:
Which of the following is the closest to \(11*10^{10}–4*10^4\)?

A. \(10^2\)
B. \(10^7\)
C. \(10^8\)
D. \(10^9\)
E. \(10^{11}\)

Which of the answer choices is closest to

\(11*10^{10}–4*10^4\)?

Factor out \(10^4\)

\(10^4(11*10^{6}) – (4*1)\)

Dismiss latter term, -4. It makes no difference with numbers this large.* Now multiply numbers in the first term to get

\(11*10^{10}\)

There are a few ways to go about this. I think the easiest is to assume that 11 is close to 10. Substitute 10 for 11, and because the prompt asks for closest to, that's the answer. The answer cannot be less than whatever we find, because 11 is greater than 10.

\(10^1 * 10^{10} = 10^{11}\)

No answer choice is greater than that. It's the closest.

ANSWER E

**You could dismiss the second term entirely; (some number in the trillions) - (10,000) makes no significant dent in the trillions' value. I did it the way I posted first, just to be sure.

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Re: Which of the following is the closest to 11*10^10–4*10^4? [#permalink]

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New post 02 Sep 2017, 01:38
MathRevolution wrote:
Which of the following is the closest to \(11*10^{10}–4*10^4\)?

A. \(10^2\)
B. \(10^7\)
C. \(10^8\)
D. \(10^9\)
E. \(10^{11}\)


\(11*10^{10}–4*10^4 = (10 + 1) * 10^{10} - 4 * 10^4 = 10^{11} + 10^{10} - 4 * 10^4\)

\(10^11 + (10^{10} - 4 * 10^4)\) is nearer to \(10^{11}\) than \(10^9\). Answer E.
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Expert Post
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Re: Which of the following is the closest to 11*10^10–4*10^4? [#permalink]

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New post 03 Sep 2017, 18:44
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=> \(4*10^4\) is relative small compared with \(11*10^{10}\). Thus we can consider \(11*10^{10}\) only.
It is close \(10^{11}\).

Ans: E
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Re: Which of the following is the closest to 11*10^10–4*10^4?   [#permalink] 03 Sep 2017, 18:44
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