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Manager  Joined: 01 Feb 2012
Posts: 85
Which of the following is closest to 4/2.001?  [#permalink]

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3 00:00

Difficulty:   35% (medium)

Question Stats: 71% (01:27) correct 29% (01:19) wrong based on 82 sessions

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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

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
Math Expert V
Joined: 02 Aug 2009
Posts: 8179
Which of the following is closest to 4/2.001?  [#permalink]

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4
fireinbelly wrote:
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.

http://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.

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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Manager  Joined: 23 Jan 2013
Posts: 128
Concentration: Technology, Other
Schools: Berkeley Haas
GMAT Date: 01-14-2015
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Re: Which of the following is closest to 4/2.001?  [#permalink]

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2
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 !!
Math Expert V
Joined: 02 Sep 2009
Posts: 59087
Re: Which of the following is closest to 4/2.001?  [#permalink]

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2
fireinbelly wrote:
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

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: $$\frac{4(2-0.001)}{4-0.001^2} \approx \frac{4(2-0.001)}{4}=2-0.001=1.999$$.

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Joined: 16 Oct 2010
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Location: Pune, India
Re: Which of the following is closest to 4/2.001?  [#permalink]

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2
fireinbelly wrote:
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?

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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Karishma
Veritas Prep GMAT Instructor

Math Expert V
Joined: 02 Aug 2009
Posts: 8179
Re: Which of the following is closest to 4/2.001?  [#permalink]

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1
fireinbelly wrote:
Bunuel wrote:
fireinbelly wrote:
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

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: $$\frac{4(2-0.001)}{4-0.001^2} \approx \frac{4(2-0.001)}{4}=2-0.001=1.999$$.

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?

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..
_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 8179
Re: Which of the following is closest to 4/2.001?  [#permalink]

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shelrod007 wrote:
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 !!

hi, you cannot assume that here since all vaues are very very close...
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Manager  Joined: 01 Feb 2012
Posts: 85
Re: Which of the following is closest to 4/2.001?  [#permalink]

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Bunuel wrote:
fireinbelly wrote:
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

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: $$\frac{4(2-0.001)}{4-0.001^2} \approx \frac{4(2-0.001)}{4}=2-0.001=1.999$$.

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?

Manager  Joined: 01 Feb 2012
Posts: 85
Re: Which of the following is closest to 4/2.001?  [#permalink]

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ok...thank you chetan2u!
Manager  Status: Kitchener
Joined: 03 Oct 2013
Posts: 87
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)
Re: Which of the following is closest to 4/2.001?  [#permalink]

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Bunuel wrote:
fireinbelly wrote:
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

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: $$\frac{4(2-0.001)}{4-0.001^2} \approx \frac{4(2-0.001)}{4}=2-0.001=1.999$$.

Dear Bunuel, how the denominator (2+0.001) become equal to (2+0.001)(2-0.001)
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Math Expert V
Joined: 02 Aug 2009
Posts: 8179
Re: Which of the following is closest to 4/2.001?  [#permalink]

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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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Manager  Joined: 01 Feb 2012
Posts: 85
Re: Which of the following is closest to 4/2.001?  [#permalink]

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VeritasPrepKarishma wrote:
fireinbelly wrote:
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?

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.

Thanks Karishma....it really helps!
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Re: Which of the following is closest to 4/2.001?  [#permalink]

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_________________ Re: Which of the following is closest to 4/2.001?   [#permalink] 22 Sep 2019, 07:51
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