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# M24-07

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Math Expert
Joined: 02 Sep 2009
Posts: 51058

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16 Sep 2014, 00:20
00:00

Difficulty:

35% (medium)

Question Stats:

75% (00:50) correct 25% (00:51) wrong based on 164 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

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Math Expert
Joined: 02 Sep 2009
Posts: 51058

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16 Sep 2014, 00:20
5
4
Official Solution:

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

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

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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21 Jul 2015, 02:57
Bunuel , I approximated the denominator as 2 and chose D as answer.It did strike that it would be a little lower than 2 as the denominator is a little over 2 but generally we approximate like i did earlier.So did we go into so much detail because the answer choices were in detail too?
Math Expert
Joined: 02 Sep 2009
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21 Jul 2015, 03:00
Ralphcuisak wrote:
Bunuel , I approximated the denominator as 2 and chose D as answer.It did strike that it would be a little lower than 2 as the denominator is a little over 2 but generally we approximate like i did earlier.So did we go into so much detail because the answer choices were in detail too?

Yes, the options are very close to each other so you should approximate with more precision.
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14 Nov 2016, 21:53
Bunuel

I'm currently going through quiz problems for gmatclub tests.

As I'm going through, I see your explanation for this kind of problem, but I don't understand.

Could you send me a reference link?

thank you
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Concentration: Finance, Entrepreneurship
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19 Aug 2017, 13:25
This is a 500 level question...?
Intern
Joined: 08 Jan 2018
Posts: 3

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25 Jan 2018, 08:00
Hi,

I don't understand the explanation. Why and how we are transforming the equation like that?

Isn't it faster to do it like me:

I just multiplied the equation by 1000, so then there is 4000/2001= and it is very easy to solve.

Thank you
Max
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Joined: 02 Jun 2015
Posts: 22
Location: United States

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18 Mar 2018, 10:49
MaxKirchmayer wrote:
Hi,

I don't understand the explanation. Why and how we are transforming the equation like that?

Isn't it faster to do it like me:

I just multiplied the equation by 1000, so then there is 4000/2001= and it is very easy to solve.

Thank you
Max

Hi Max,

To make this calculation easier let's round down 2.001 to 2.

Then it will be 4/2 = 2

But, we know that the larger the denominator, the smaller is the number.

Comparing: 4/2.001 is a little bit smaller than 4/2.

This way, the answer choice has to be a little bit smaller than 2.

The answer is 1.999 ( C ).

I hope it helps!

Thanks, Ale
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16 Apr 2018, 01:47
+1 for option C.
Got it by brute force solving though ....
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19 Apr 2018, 19:25
1
Bunuel, I understand your explanation. I don't understand how are we meant to look at the original fraction and think of difference of squares - Is this theory I've missed (likely) or something completely outside the box?
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09 Jun 2018, 04:27
1
philipssonicare wrote:
Bunuel, I understand your explanation. I don't understand how are we meant to look at the original fraction and think of difference of squares - Is this theory I've missed (likely) or something completely outside the box?

Hi @Bunnel,
I too have same doubt as above. Pls explain .
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11 Aug 2018, 14:07
I asked a Chinese friend about this question and she said that approaching a fraction by splitting the denominator and using difference of squares was something she remembers from school. Clearly it's not something that we remember from school in other countries.

Bunuel, please tell me what area of maths to look up for questions like this or refer me to questions that take a similar approach.
Re: M24-07 &nbs [#permalink] 11 Aug 2018, 14:07
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# M24-07

Moderators: chetan2u, Bunuel

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