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Which of the following is closest to the value of 999/(100+1/999)?
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Updated on: 08 Oct 2019, 06:36
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
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.
Last edited by Bunuel on 08 Oct 2019, 06:36, edited 2 times in total.
RENAMED THE TOPIC.
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Which of the following is closest to the value of 999/(100+1/999)?
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Updated on: 14 Apr 2022, 14:55
Updated on: 14 Apr 2022, 14:55
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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
a. 10
b. 1
c. 0.1
d. 0.01
e. 0.001
This question is a great example of using the answer choices to our advantage.
When we check the answer choices, we see that we have a gigantic spread.
For example, 10 is 900% greater than 1, which is 900% greater than 0.1, which is 900% greater than 0.01, which is 900% greater than 0.001.
In comparison to the significant differences between each answer choice, I'm going to make some a incredibly minor changes to the values in our calculation.
\(\frac{999}{100+\frac{1}{999}} ≈ \frac{1000}{100} ≈ 10\)
Answer: A
Aside:
Changing \(999\) to \(1000\) represents a change of approximately 0.1%
Similarly, changing \(100+\frac{1}{999}\) to \(100\) represents a change of approximately 0.001%.
Originally posted by BrentGMATPrepNow on 26 Jan 2016, 13:09.
Last edited by BrentGMATPrepNow on 14 Apr 2022, 14:55, edited 2 times in total.
Last edited by BrentGMATPrepNow on 14 Apr 2022, 14:55, edited 2 times in total.
Re: Which of the following is closest to the value of 999/(100+1/999)?
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26 Jan 2016, 12:53
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
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
