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Which of the following is closest to 4/2.001? Updated on: 11 Oct 2025, 11:17
Originally posted by Bunuel on 08 Feb 2015, 02:44.
Last edited by Bunuel on 11 Oct 2025, 11:17, edited 1 time in total.
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Which of the following is closest to \(\frac{4}{2.001}\)?

A. 1.997
B. 1.998
C. 1.999
D. 2.000
E. 2.001


M24-07

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Which of the following is closest to 4/2.001? 08 Feb 2015, 04:15
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Which of the following is closest to \(\frac{4}{2.001}\)?

A. 1.997
B. 1.998
C. 1.999
D. 2.000
E. 2.001


The answer options are extremely close to each other, necessitating a very precise calculation. We can't simply round off 2.001 to 2 and assert that \(\frac{4}{2.001}\) is closest to 2 from the options given, due to this small difference.

Let's express 2.001 as 2 + 0.001 and multiply both the numerator and the denominator by the conjugate, 2 - 0.001:

    \(\frac{4}{2.001}=\)

    \(=\frac{4}{2+0.001}=\)

    \(=\frac{4(2-0.001)}{(2+0.001)(2-0.001)}=\)

    \(=\frac{4(2-0.001)}{4-0.001^2}\).

Now, \(0.001^2=0.000001\) is a very small number. Compared to 4, this value is practically negligible (do note that while we couldn't ignore 0.001 earlier, we can overlook 0.000001 now because it is 1000 times smaller than 0.001). Hence, we can approximate the equation as:

    \(\frac{4(2-0.001)}{4-0.001^2} \approx \)

    \(\approx \frac{4(2-0.001)}{4}=\)

    \(= 2-0.001 =\)

    \(=1.999\).

Therefore, \(\frac{4}{2.001}\) is closest to 1.999 among the provided options.

Answer: C
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Which of the following is closest to 4/2.001? 08 Feb 2015, 02:50
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Hope this helps

Which of the following is closest to 4/2.001?

(A) 1.997
(B) 1.998
(C) 1.999
(D) 2.000
(E) 2.001

We are asked 4/2.001 is closest to what , hence we cannot assume or ignore the 0.001 as extremely small .

We would need to consider it . Back to the question

4 is divided by a number 2 the answer would be 2 exactly . In this case 4 is divided by a number which is slightly bigger than 2 i.e 2.001

Hence by value = ( numerator / denominator ) if the denominator increases the value would decrease .

In this case since denominator has increased by 0.001 the value would decrease slightly to less than 2 and hence the answer would be 1.999 .

Hope my explanation helps !!
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Which of the following is closest to 4/2.001? 08 Feb 2015, 03:05
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fireinbelly
This question is already posted on the following thread however the thread is locked and I am not able to reply there. Infact I searched however could not find any other discussion around this question...hence posting it here.

https://gmatclub.com/forum/m24-q-7-expla ... 76513.html

Which of the following is closest to 4/2.001?

(A) 1.997
(B) 1.998
(C) 1.999
(D) 2.000
(E) 2.001

I have seen some questions where if the value is .001 or very small value then we usually ignore that value...however the answer seems to be C? why cant we say that 4/2.001 is very close to 4/2 as .001 is negligible here hence the answer would be D in that case. Can someone please help me understanding this concept? Thanks.
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hi ,
I'll suggest you a slightly more accurate way to do this..
\(\frac{4}{2.001}=\frac{4}{2+0.001}\))..
multiply both numerator and denominator by 2-.001
\(\frac{4(2-0.001)}{(2+0.001)(2-0.001)}\)
=\(\frac{4(1.999)}{(4-0.000001)}\)....
0.000001 being very small can be neglected, so the equation becomes..
\(\frac{4(1.999)}{4}=1.999\) ans C
hope it helped
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Which of the following is closest to 4/2.001? 08 Feb 2015, 03:06
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shelrod007
Hope this helps

Which of the following is closest to 4/2.001?

(A) 1.997
(B) 1.998
(C) 1.999
(D) 2.000
(E) 2.001

We are asked 4/2.001 is closest to what , hence we cannot assume or ignore the 0.001 as extremely small .

We would need to consider it . Back to the question

4 is divided by a number 2 the answer would be 2 exactly . In this case 4 is divided by a number which is slightly bigger than 2 i.e 2.001

Hence by value = ( numerator / denominator ) if the denominator increases the value would decrease .

In this case since denominator has increased by 0.001 the value would decrease slightly to less than 2 and hence the answer would be 1.999 .

Hope my explanation helps !!
Show more

hi, you cannot assume that here since all vaues are very very close...
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Which of the following is closest to 4/2.001? 08 Feb 2015, 05:07
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Which of the following is closest to \(\frac{4}{2.001}\)?

A. 1.997
B. 1.998
C. 1.999
D. 2.000
E. 2.001

Show Spoiler
I have seen some questions where if the value is .001 or very small value then we usually ignore that value...however the answer seems to be C? why cant we say that 4/2.001 is very close to 4/2 as .001 is negligible here hence the answer would be D in that case. Can someone please help me understanding this concept? Thanks.


M24-07


\(\frac{4}{2.001}=\frac{4}{2+0.001}=\frac{4(2-0.001)}{(2+0.001)(2-0.001)}=\frac{4(2-0.001)}{4-0.001^2}\).

Now, since \(0.001^2\) is very small number then \(4-0.001^2\) is very close to 4 itself, so \(0.001^2\) is basically negligible in this case and we can write: \(\frac{4(2-0.001)}{4-0.001^2} \approx \frac{4(2-0.001)}{4}=2-0.001=1.999\).

Answer: C.
Show more

Hi Bunuel,

Thanks for the solution. I understood the way to approach it and why the answer is C.

I have a small query - while solving as you mentioned that 4 - 0.002^2 is equal to 4 only because 0.002^2 is negligible here....However in the main question where 2 - 0.002 is written 0.002 is not negligible.
Is it not negligible only because it is not sufficiently smaller no.? If it were 0.002^2 in the main question instead of 0.002 then could that have been negligible?

Please share your valuable inputs.
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Which of the following is closest to 4/2.001? 08 Feb 2015, 05:24
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fireinbelly
Bunuel
fireinbelly
Which of the following is closest to \(\frac{4}{2.001}\)?

A. 1.997
B. 1.998
C. 1.999
D. 2.000
E. 2.001

Show Spoiler
I have seen some questions where if the value is .001 or very small value then we usually ignore that value...however the answer seems to be C? why cant we say that 4/2.001 is very close to 4/2 as .001 is negligible here hence the answer would be D in that case. Can someone please help me understanding this concept? Thanks.


M24-07


\(\frac{4}{2.001}=\frac{4}{2+0.001}=\frac{4(2-0.001)}{(2+0.001)(2-0.001)}=\frac{4(2-0.001)}{4-0.001^2}\).

Now, since \(0.001^2\) is very small number then \(4-0.001^2\) is very close to 4 itself, so \(0.001^2\) is basically negligible in this case and we can write: \(\frac{4(2-0.001)}{4-0.001^2} \approx \frac{4(2-0.001)}{4}=2-0.001=1.999\).

Answer: C.

Hi Bunuel,

Thanks for the solution. I understood the way to approach it and why the answer is C.

I have a small query - while solving as you mentioned that 4 - 0.002^2 is equal to 4 only because 0.002^2 is negligible here....However in the main question where 2 - 0.002 is written 0.002 is not negligible.
Is it not negligible only because it is not sufficiently smaller no.? If it were 0.002^2 in the main question instead of 0.002 then could that have been negligible?

Please share your valuable inputs.
Show more
hi fireinbelly,
if i may try to explain you..
look at the answer values they are varying to .001(for eg 2.000 or 1.999 or 1.998)... so yes .001 is important here....
but .001^2=.000001, which is way to small as compared to .001 .... so can be left..
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Which of the following is closest to 4/2.001? 08 Feb 2015, 05:30
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ok...thank you chetan2u!
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Which of the following is closest to 4/2.001? 08 Feb 2015, 08:40
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Bunuel
fireinbelly
Which of the following is closest to \(\frac{4}{2.001}\)?

A. 1.997
B. 1.998
C. 1.999
D. 2.000
E. 2.001

Show Spoiler
I have seen some questions where if the value is .001 or very small value then we usually ignore that value...however the answer seems to be C? why cant we say that 4/2.001 is very close to 4/2 as .001 is negligible here hence the answer would be D in that case. Can someone please help me understanding this concept? Thanks.


M24-07


\(\frac{4}{2.001}=\frac{4}{2+0.001}=\frac{4(2-0.001)}{(2+0.001)(2-0.001)}=\frac{4(2-0.001)}{4-0.001^2}\).

Now, since \(0.001^2\) is very small number then \(4-0.001^2\) is very close to 4 itself, so \(0.001^2\) is basically negligible in this case and we can write: \(\frac{4(2-0.001)}{4-0.001^2} \approx \frac{4(2-0.001)}{4}=2-0.001=1.999\).

Answer: C.
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Dear Bunuel, how the denominator (2+0.001) become equal to (2+0.001)(2-0.001)
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Which of the following is closest to 4/2.001? 08 Feb 2015, 08:56
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Dear Bunuel, how the denominator (2+0.001) become equal to (2+0.001)(2-0.001)[/quote]

hi,
both denominator and numerator are multiplied by (2-.001) to basically simploiify the equation
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Which of the following is closest to 4/2.001? 09 Feb 2015, 01:39
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fireinbelly

I have a small query - while solving as you mentioned that 4 - 0.002^2 is equal to 4 only because 0.002^2 is negligible here....However in the main question where 2 - 0.002 is written 0.002 is not negligible.
Is it not negligible only because it is not sufficiently smaller no.? If it were 0.002^2 in the main question instead of 0.002 then could that have been negligible?

Please share your valuable inputs.
Show more

Responding to a pm:

I think you got your answer. Whether something is negligible depends on with what we are comparing it. When working with 1.999 and 2.001, then .001 is not negligible. But .000001 is. Similarly, if the options were far apart such as 2, 3 etc then we know that we can ignore .001.
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Which of the following is closest to 4/2.001? 12 Feb 2023, 08:30
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Re: Which of the following is closest to 4/2.001?

I used Numbers concept: Not sure if its the right approach though.

Multiply both Numerator and denominator by 1000

4000/2001= Since the denominator is not of the form 2^m * 5^n The decimal will not terminate.

Looking at the options Only C is Non terminating
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Which of the following is closest to 4/2.001? 01 May 2026, 08:33
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Looking at the options we can easily rule out D and E.
Now we dont know how much smaller than 2 it is:
Naturally lets take 1.999 as it is the closest to 2.

Assume 1.999 is true and you will notice that if it is true, it must be very close to 4:

1.999*2.001 = (2-10^-3)(2+10^-3) = 4-10^-6.
Now this is extremely close to 4. There can't possibly be any other number as we took the immediate value below 2.
So our answer is 1.999.

Answer: Option C

__________________________

I tried using the mathematical induction method here to get to the answer faster. However it could be a risky approach because in time crunch situation, the answer you assume to be true might not be true but one might still go for it because you might confuse the right answer with presumptions.
Bunuel
Which of the following is closest to \(\frac{4}{2.001}\)?

A. 1.997
B. 1.998
C. 1.999
D. 2.000
E. 2.001


M24-07

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