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

Question

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

Bunuel · Accepted Answer

Which of the following is closest to  \frac{1}{1.001} ?

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

\frac{1}{1.001} = \frac{1}{1 + 0.001} .
 
Multiply the above by  \frac{1 - 0.001}{1 - 0.001} :
 
 \frac{1 - 0.001}{(1 + 0.001)(1 - 0.001)} =\frac{1 - 0.001}{1 - 0.001^2}  .
 
Now, because  0.001^2  is very small,  1 - 0.001^2  is very close to 1. Therefore,  \frac{1 - 0.001}{1 - 0.001^2} \approx \frac{1 - 0.001}{1} = 1 - 0.001 = 0.999 .

Answer: C

abhijitatprepitt · Answer

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.

egghead2017 · Answer

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

shashankism · Answer

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.

JeffTargetTestPrep · Answer

We can convert 1.001 to a fraction and we have:

1/  = 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

4d · Answer

1000/1001 > 999/1000

Hence C

KarishmaB · Answer

\frac{1}{1.001} = \frac{1000}{1001} which is slightly less than 1. .999 = \frac{999}{1000} which is slightly less than 1 too. When we add 1 to both the numerator and denominator of 999/1000, we get 1000/1001. This number will be closer to 1 than 999/1000. So on the number line, we have .997, .998, .999, 1000/1001, 1.000, 1.001 in that order. Closest to 1000/1001 is either .999 or 1. From 999/1000, we go to 1000/1001 by adding 1 to both numerator and denominator. But from 1000/1001 to 1, we go by adding 1 to numerator alone. So 1 will be much greater than 1000/1001 (relatively speaking). Hence closest to 1000/1001 is .999. Answer (C) Check this post for this concept: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... round-one/

Vijay_K · Answer

D&E can be eliminated since answer cant be 1 or greater than 1.

Whenever you divide the number 1/1.1 0r 10/11 or 100/111 or 1/1.01 or 1/1.001 or 1/1.0001 it will always have the repetition value  9s  in their decimal and  it won't contain any such numbers as 8s or 7s in their decimal . That leads to straightaway option C.

bumpbot · Answer

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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)?

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