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Which of the following is closest to (1)/(1.001)?

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Which of the following is closest to (1)/(1.001)?  [#permalink]

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New post 10 May 2017, 12:47
1
3
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

72% (00:53) correct 28% (00:38) wrong based on 75 sessions

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Which of the following is closest to (1)/(1.001)?

A. 0.997
B. 0.998
C. 0.999
D. 1.000
E. 1.001

This question has been posted previously; however, the thread is short and discontinued. I'm looking for a clear approach for solving this type of problem besides back-solving. Thanks!
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Re: Which of the following is closest to (1)/(1.001)?  [#permalink]

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New post 10 May 2017, 13:09
2
Cez005 wrote:
Which of the following is closest to (1)/(1.001)?

A. 0.997
B. 0.998
C. 0.999
D. 1.000
E. 1.001

This question has been posted previously; however, the thread is short and discontinued. I'm looking for a clear approach for solving this type of problem besides back-solving. Thanks!


Back solving seems the best way. Since you can eliminate D and E from the get go start with C. Back-solving should be easy because multiplications are with 1.

Another approach could be a little bit of factoring:


1/1.001 = 1000/1001 = (1001-1)/1001 = 1 - 1/1001 ~ 1 - 0.001 ~ 0.999. Since there is approximation inherent in the last two steps of this approach, I would be cautious.
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Re: Which of the following is closest to (1)/(1.001)?  [#permalink]

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New post 11 May 2017, 04:30
We straight away ignore the options D and E as they are greater than 1, because in the above fraction the denominator is greater the numerator. Of the remaining, the answer should be C
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Re: Which of the following is closest to (1)/(1.001)?  [#permalink]

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New post 11 May 2017, 04:48
egghead2017 wrote:
We straight away ignore the options D and E as they are greater than 1, because in the above fraction the denominator is greater the numerator. Of the remaining, the answer should be C

Since the question is asking that which is closest to 1/1.001. We can't just eliminate D & E. Though we can eliminate E in comparison to D. But there might be a possibility that 1/1.001 may be closest to 1 also..
So we will have to check it by solving or other methods.
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Re: Which of the following is closest to (1)/(1.001)?  [#permalink]

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New post 15 May 2017, 17:26
Cez005 wrote:
Which of the following is closest to (1)/(1.001)?

A. 0.997
B. 0.998
C. 0.999
D. 1.000
E. 1.001


We can convert 1.001 to a fraction and we have:

1/[(1001/1000)] = 1000/1001

It is obvious that this number is just a little smaller than 1 (which makes it just a little greater than 0.999), so the answer is either D or C. We must decide which. We will compare the difference between 1 and 1000/1001 to the difference between 1000/1001 and 0.999 = 999/1000.

1 - 1000/1001 = 1000/1000 - 1000/1001

= 1001000/1001000 - 1000000/1001000

= 1000/1001000

= 1/1001

1000/1001 - 999/1000 = 1000000/1001000 - 999999/1001000

= 1/1001000

Since the difference between 1000/1001 and 999/1000 is much smaller than the difference between 1 and 1000/1001, 1000/1001 is closer to 999/1000 = 0.999 than any other choice.

Answer: C
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Re: Which of the following is closest to (1)/(1.001)?  [#permalink]

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New post 22 Oct 2018, 21:55
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Re: Which of the following is closest to (1)/(1.001)? &nbs [#permalink] 22 Oct 2018, 21:55
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