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Which of the following is closest to the value of 999/(100+1/999)?

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Which of the following is closest to the value of 999/(100+1/999)?  [#permalink]

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New post Updated on: 08 Oct 2019, 06:36
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Which of the following is closest to the value of \(\frac{999}{100+\frac{1}{999}}\)?

a. 10
b. 1
c. 0.1
d. 0.01
e. 0.001

Originally posted by paidlukkha on 26 Jan 2016, 10:30.
Last edited by Bunuel on 08 Oct 2019, 06:36, edited 2 times in total.
RENAMED THE TOPIC.
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Re: Which of the following is closest to the value of 999/(100+1/999)?  [#permalink]

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New post 26 Jan 2016, 13:09
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paidlukkha wrote:
Which of the following is closest to the value of \(\frac{999}{100+1/999}\)?

a. 10
b. 1
c. 0.1
d. 0.01
e. 0.001


As with all math questions, ALWAYS CHECK THE ANSWER CHOICES BEFORE STARTING YOUR SOLUTION.
For more on this, see our free video: http://www.gmatprepnow.com/module/gener ... video/1111

Here the answer choices are well spread apart, which means we can use some AGGRESSIVE estimation:
999/(100 + 1/999) ≈ 1000/(100)
≈ 10
Answer: A

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Re: Which of the following is closest to the value of 999/(100+1/999)?  [#permalink]

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New post 26 Jan 2016, 12:53
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Good exercise in approximation.

We can approximate the numerator to be 1000.
For the denominator, 1/999 is MUCH less than 100, so we can disregard it completely. (1/999 = 0.001001..., so 100.001 ≈ 100)
The expression now becomes 1000/100 = 10

Answer: A
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Re: Which of the following is closest to the value of 999/(100+1/999)?  [#permalink]

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New post 12 Oct 2017, 14:09
Is there a way to solve this using the (a+b)(a-b) construction? I've seen problems similar to this in the past where you used the sum of perfect squares strategy. Or is approximation the best way to solve since we don't need to solve for an exact number?
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Re: Which of the following is closest to the value of 999/(100+1/999)?  [#permalink]

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New post 05 Oct 2018, 14:39
Hi All,

We're asked which of the following numbers is closest to the value of the given fraction. While it might appear that some of the answers are 'close' to one another, the reality is that each answer is 10 TIMES greater than the answer immediately below it - meaning that we can use estimation to answer this question (and avoid any step-heavy calculations).

This fraction can be rewritten as approximately 1000/100 = 10. From a logical standpoint, that's the only answer that's even remotely close - so it must be the answer.

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Re: Which of the following is closest to the value of 999/(100+1/999)?   [#permalink] 05 Oct 2018, 14:39
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