|
Author |
Message |
|
VP
Joined: 05 Jul 2008
Posts: 1442
Followers: 28
Kudos [?]:
152
[9] , given: 1
|
M24 Q 7 explanation [#permalink]
 12 Mar 2009, 14:49
9
This post received
KUDOS
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 Source: GMAT Club Tests - hardest GMAT questions 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
|
|
|
|
|
|
|
|
|
SVP
Joined: 07 Nov 2007
Posts: 1842
Location: New York
Followers: 20
Kudos [?]:
291
[4] , given: 5
|
Re: M24 Q 7 explanation [#permalink]
12 Mar 2009, 19:10
4
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
|
|
|
|
|
|
Manager
Joined: 26 Nov 2009
Posts: 180
Followers: 3
Kudos [?]:
49
[1] , given: 5
|
Re: M24 Q 7 explanation [#permalink]
04 Jan 2010, 07:42
1
This post received
KUDOS
I guessed this and got it wrong we can easily eliminate choice D and E. but I feel the official explanation is good but not great because it may lead to traps as the difference in answer choices are too narrow and small. I tried to solve it arithematically and got the answer in less than 2 mins but I was not in any pressure to solve this in less than 2 mins 
|
|
|
|
|
|
VP
Joined: 05 Jul 2008
Posts: 1442
Followers: 28
Kudos [?]:
152
[0], given: 1
|
Re: M24 Q 7 explanation [#permalink]
12 Mar 2009, 19:46
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).
|
|
|
|
|
|
Manager
Joined: 23 Nov 2009
Posts: 58
Followers: 1
Kudos [?]:
9
[0], given: 1
|
Re: M24 Q 7 explanation [#permalink]
04 Jan 2010, 17:07
I got C by solving arithematically in under 2 mins
_________________
A kudos would greatly help
Tuhin
|
|
|
|
|
|
Intern
Joined: 28 Sep 2009
Posts: 38
Location: Toronto, Ontario, Canada
Followers: 0
Kudos [?]:
0
[0], given: 2
|
Re: M24 Q 7 explanation [#permalink]
04 Jan 2010, 20:24
I got it right too
|
|
|
|
|
|
Manager
Joined: 01 Jan 2011
Posts: 92
Schools: INSEAD,IIMA,IIMB
Followers: 0
Kudos [?]:
0
[0], given: 2
|
Re: M24 Q 7 explanation [#permalink]
10 Jan 2011, 06:31
why is D and E given...C would gt the call within 2 minutes
_________________
_________________________
Try and you will succeed !
|
|
|
|
|
|
Manager
Joined: 26 Dec 2009
Posts: 151
Location: United Kingdom
Concentration: Strategy, Technology
GMAT 1: 500 Q45 V16
WE: Consulting (Computer Software)
Followers: 2
Kudos [?]:
12
[0], given: 10
|
Re: M24 Q 7 explanation [#permalink]
10 Jan 2011, 07:09
slved arithematically. but thanks for the explanation
|
|
|
|
|
|
Manager
Joined: 01 Nov 2010
Posts: 204
Location: India
Concentration: Technology, Marketing
GMAT Date: 08-27-2012
GPA: 3.8
WE: Marketing (Manufacturing)
Followers: 5
Kudos [?]:
10
[0], given: 26
|
Re: M24 Q 7 explanation [#permalink]
10 Jan 2011, 09:18
OE is good. C is the answer.
_________________
kudos me if you like my post.
Attitude determine everything.
all the best and God bless you.
|
|
|
|
|
|
Intern
Joined: 29 Oct 2010
Posts: 3
Followers: 0
Kudos [?]:
1
[0], given: 1
|
Re: M24 Q 7 explanation [#permalink]
10 Jan 2011, 11:43
got it right 
|
|
|
|
|
|
Manager
Joined: 19 Oct 2010
Posts: 242
Location: India
Concentration: Marketing, Finance
GMAT 1: 560 Q36 V31
GPA: 3
Followers: 5
Kudos [?]:
10
[0], given: 21
|
Re: M24 Q 7 explanation [#permalink]
22 Feb 2011, 11:45
I guessed, got it right. Tried solving it and got it wrong!!!
_________________
petrifiedbutstanding
|
|
|
|
|
|
Director
Joined: 01 Feb 2011
Posts: 792
Followers: 11
Kudos [?]:
63
[0], given: 42
|
Re: M24 Q 7 explanation [#permalink]
11 Jun 2011, 15:43
(4/(2+0.001))*((2-0.001)/(2-0.001))
=(4/(2^2-0.001^2)))*(1.999)
= 1.999 as first part's denominator is very close to 4 as 0.001^2 is very small.
Answer is C.
|
|
|
|
|
|
Senior Manager
Joined: 08 Jun 2010
Posts: 400
Location: United States
Concentration: General Management, Finance
GMAT 1: 680 Q50 V32
Followers: 1
Kudos [?]:
37
[0], given: 13
|
Re: M24 Q 7 explanation [#permalink]
12 Jan 2012, 06:12
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.
|
|
|
|
|
|
Director
Status: Final Countdown
Joined: 17 Mar 2010
Posts: 566
Location: India
GPA: 3.82
WE: Account Management (Retail Banking)
Followers: 10
Kudos [?]:
68
[0], given: 75
|
Re: M24 Q 7 explanation [#permalink]
12 Jan 2012, 10:15
OE has the best explanation
_________________
" Make more efforts "
Press Kudos if you liked my post
|
|
|
|
|
|
Intern
Joined: 06 Jan 2012
Posts: 28
Concentration: Finance, General Management
GMAT Date: 04-16-2012
GPA: 3
WE: Information Technology (Computer Software)
Followers: 2
Kudos [?]:
18
[0], given: 3
|
Re: M24 Q 7 explanation [#permalink]
13 Jan 2012, 17:03
icandy 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 Source: 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.
|
|
|
|
|
|
Intern
Joined: 23 Aug 2012
Posts: 13
Followers: 0
Kudos [?]:
0
[0], given: 8
|
Re: M24 Q 7 explanation [#permalink]
30 Aug 2012, 17:25
vkredi wrote: icandy 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 Source: 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?
|
|
|
|
|
|
Senior Manager
Joined: 08 Jun 2010
Posts: 400
Location: United States
Concentration: General Management, Finance
GMAT 1: 680 Q50 V32
Followers: 1
Kudos [?]:
37
[0], given: 13
|
Re: M24 Q 7 explanation [#permalink]
30 Aug 2012, 20:02
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.
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11594
Followers: 1799
Kudos [?]:
9586
[0], given: 826
|
Re: M24 Q 7 explanation [#permalink]
14 Jan 2013, 06:36
icandy 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 Source: GMAT Club Tests - hardest GMAT questions 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 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. Answer: C.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Intern
Joined: 25 Dec 2012
Posts: 38
Followers: 0
Kudos [?]:
0
[0], given: 6
|
Re: M24 Q 7 explanation [#permalink]
14 Jan 2013, 07:08
2.001 = 2 ( 1 + (10^-3)/2)
1/(x+a) = (x+a)^-1 = x-a
4/2.001 = 4/ 2 ( 1 + (10^-3)/2) = 2 ( 1 - (10^-3)/2) = 2 - 0.001 = 1.999
|
|
|
|
|
|
Intern
Joined: 11 Jul 2012
Posts: 13
Concentration: Entrepreneurship, Marketing
GPA: 3.21
Followers: 0
Kudos [?]:
2
[0], given: 21
|
Re: M24 Q 7 explanation [#permalink]
14 Jan 2013, 09:54
icandy 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 Source: GMAT Club Tests - hardest GMAT questions 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 _________________
all you need is a will.
|
|
|
|
|
|
|
Re: M24 Q 7 explanation
[#permalink]
14 Jan 2013, 09:54
|
|
|
|
|
|
|
|
|
|
|
close
