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# Which of the following is closest to 4/2.001?

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Manager
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Which of the following is closest to 4/2.001?  [#permalink]

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08 Feb 2015, 02:44
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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
Joined: 02 Aug 2009
Posts: 8179
Which of the following is closest to 4/2.001?  [#permalink]

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08 Feb 2015, 03:05
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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Concentration: Technology, Other
Schools: Berkeley Haas
GMAT Date: 01-14-2015
WE: Information Technology (Computer Software)
Re: Which of the following is closest to 4/2.001?  [#permalink]

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08 Feb 2015, 02:50
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
Joined: 02 Sep 2009
Posts: 59087
Re: Which of the following is closest to 4/2.001?  [#permalink]

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08 Feb 2015, 04:15
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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Re: Which of the following is closest to 4/2.001?  [#permalink]

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09 Feb 2015, 01:39
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
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Math Expert
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Posts: 8179
Re: Which of the following is closest to 4/2.001?  [#permalink]

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08 Feb 2015, 05:24
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..
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Math Expert
Joined: 02 Aug 2009
Posts: 8179
Re: Which of the following is closest to 4/2.001?  [#permalink]

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08 Feb 2015, 03:06
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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08 Feb 2015, 05:07
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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08 Feb 2015, 05:30
ok...thank you chetan2u!
Manager
Status: Kitchener
Joined: 03 Oct 2013
Posts: 87
Concentration: Finance, Finance
GPA: 2.9
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Re: Which of the following is closest to 4/2.001?  [#permalink]

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08 Feb 2015, 08:40
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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Re: Which of the following is closest to 4/2.001?  [#permalink]

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08 Feb 2015, 08:56
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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Re: Which of the following is closest to 4/2.001?  [#permalink]

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10 Feb 2015, 02:52
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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22 Sep 2019, 07:51
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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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