Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If a is small, \frac{4}{2 + a} is close to 2 - a . This is because (2 - a)(2 + a) = 4 - a^2 , which is close to 4 if a is small. So, \frac{4}{2.001} = \frac{4}{2 + 0.001} is approximately 2 - 0.001 = 1.999 . The correct answer is C.

I am posting the OE because I did not understand the OE. I arrived at the solution though. I need to understand the above logic of

Re: M24 Q 7 explanation [#permalink]
12 Mar 2009, 18:10

6

This post received KUDOS

icandy wrote:

Which of the following is closest to \frac{4}{2.001} ?

(C) 2008 GMAT Club - m24#7

* 1.997 * 1.998 * 1.999 * 2.000 * 2.001

If a is small, \frac{4}{2 + a} is close to 2 - a . This is because (2 - a)(2 + a) = 4 - a^2 , which is close to 4 if a is small. So, \frac{4}{2.001} = \frac{4}{2 + 0.001} is approximately 2 - 0.001 = 1.999 . The correct answer is C.

I am posting the OE because I did not understand the OE. I arrived at the solution though. I need to understand the above logic of

4/2+a is close to 2-a

4/(2+a) = {4*(2-a)}/ {(2+a)(2-a)} = 4(2-a)/{4-a^2} ~ 4(2-a)/4 = 2-a

since a is too small.. a^2 .. is negligible.. ~zero. _________________

Your attitude determines your altitude Smiling wins more friends than frowning

Re: M24 Q 7 explanation [#permalink]
12 Mar 2009, 18:46

x2suresh wrote:

icandy wrote:

Which of the following is closest to \frac{4}{2.001} ?

(C) 2008 GMAT Club - m24#7

* 1.997 * 1.998 * 1.999 * 2.000 * 2.001

If a is small, \frac{4}{2 + a} is close to 2 - a . This is because (2 - a)(2 + a) = 4 - a^2 , which is close to 4 if a is small. So, \frac{4}{2.001} = \frac{4}{2 + 0.001} is approximately 2 - 0.001 = 1.999 . The correct answer is C.

I am posting the OE because I did not understand the OE. I arrived at the solution though. I need to understand the above logic of

4/2+a is close to 2-a

4/(2+a) = {4*(2-a)}/ {(2+a)(2-a)} = 4(2-a)/{4-a^2} ~ 4(2-a)/4 = 2-a

since a is too small.. a^2 .. is neglible.. ~zero.

K Thanks. Essentially, the solution is equating 4 and (4-a^2).

Re: M24 Q 7 explanation [#permalink]
12 Jan 2012, 05:12

2

This post received KUDOS

Alternative method, D and E are not possible since denominator >2. So, pick the value in the center, 1.998 and multiply by 2.001 = 3.997998. Since number is less than 4. Answer is C.

If a is small, \frac{4}{2 + a} is close to 2 - a . This is because (2 - a)(2 + a) = 4 - a^2 , which is close to 4 if a is small. So, \frac{4}{2.001} = \frac{4}{2 + 0.001} is approximately 2 - 0.001 = 1.999 . The correct answer is C.

I am posting the OE because I did not understand the OE. I arrived at the solution though. I need to understand the above logic of

4/2+a is close to 2-a

My approach was (I had to think a while - I did not solve this in 2 mins)

4/2.001 = (2.001+1.999)/2.001 which then = 1 + (1.999/2.001)

Now I definitely know that the 2nd part is less than 1 and is equal to 1999/2001.

Courtesy of Manhattan GMAT FDP => If the fraction is originally smaller than 1, the fraction increases in value as it approaches 1. ie., 10/11 < 11/12 < 1011/1012 Taking it in reverse 1011/1012 > 11/12 > 10/11

In our case 1999/2001 > 999/1001 (subtracting 1000) Instead subtract 1001 to get 998/1000. Now 1999/2001 > 998/1000 (0.998)

The 2nd part now is less than 1 and greater then 0.998 which gives our answer C.

If a is small, \frac{4}{2 + a} is close to 2 - a . This is because (2 - a)(2 + a) = 4 - a^2 , which is close to 4 if a is small. So, \frac{4}{2.001} = \frac{4}{2 + 0.001} is approximately 2 - 0.001 = 1.999 . The correct answer is C.

I am posting the OE because I did not understand the OE. I arrived at the solution though. I need to understand the above logic of

4/2+a is close to 2-a

My approach was (I had to think a while - I did not solve this in 2 mins)

4/2.001 = (2.001+1.999)/2.001 which then = 1 + (1.999/2.001)

Now I definitely know that the 2nd part is less than 1 and is equal to 1999/2001.

Courtesy of Manhattan GMAT FDP => If the fraction is originally smaller than 1, the fraction increases in value as it approaches 1. ie., 10/11 < 11/12 < 1011/1012 Taking it in reverse 1011/1012 > 11/12 > 10/11

In our case 1999/2001 > 999/1001 (subtracting 1000) Instead subtract 1001 to get 998/1000. Now 1999/2001 > 998/1000 (0.998)

The 2nd part now is less than 1 and greater then 0.998 which gives our answer C.

I like your thinking and I think it's all correct, except how would you know whether 1+1999/2001 is closer to 2.000 or to 1.999?

Re: M24 Q 7 explanation [#permalink]
30 Aug 2012, 19:02

Another simple method guys:

4/(2.001) = 4/(2+0.001)

Multiply top and bottom by (2-0.001) The formula here is (a-b)(a+b) = a^2-b^2. We have all learnt this from OG.

^ denotes: raised to the power of

You get 4(2-0.001)/(2^2 - (10^-3)^2)

The denominator can be rounded off to 4 because 10^-6 is negligeble; ateast compared 10^-3 in the numerator.

So the equation shortens to : 4 (2-0.001)/(4) = 2-0.001 = 1.999.

This method is beautiful because it doesn't need any of the hardcore maths and uses only the techniques described in the OG. I hope this answers the question whether the answer is closer to 1.999 or 2.000. It is obviously closer to 1.999 because the 10^-6 is negligeble compared to 10^-3.

If a is small, \frac{4}{2 + a} is close to 2 - a . This is because (2 - a)(2 + a) = 4 - a^2 , which is close to 4 if a is small. So, \frac{4}{2.001} = \frac{4}{2 + 0.001} is approximately 2 - 0.001 = 1.999 . The correct answer is C.

I am posting the OE because I did not understand the OE. I arrived at the solution though. I need to understand the above logic of

4/2+a is close to 2-a

Which of the following is closest to \frac{4}{2.001}?

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.

If a is small, \frac{4}{2 + a} is close to 2 - a . This is because (2 - a)(2 + a) = 4 - a^2 , which is close to 4 if a is small. So, \frac{4}{2.001} = \frac{4}{2 + 0.001} is approximately 2 - 0.001 = 1.999 . The correct answer is C.

I am posting the OE because I did not understand the OE. I arrived at the solution though. I need to understand the above logic of

4/2+a is close to 2-a

Just go by the gut. 4/2 would be 2 so D and E are gone. And since the denominator is slightly bigger, the result would be minutely less than 2. Thus, 1.999. _________________

1.999*2.001 has the structure of (2-a)(2+a) = 4-a2 (a=0.001) In A and B, the products of 2.001 with 1.998 and 1.997 are smaller than that in C-> A and B are out

Eliminate E for the same reason when compared with D. D = 2*2.001 = 4+0.002. 0.002 > (0.001)^2 -> choose C