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16 Sep 2014, 01:20
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
68% (01:21) correct
32%
(01:05)
wrong
based on 353
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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
A. 1.997
B. 1.998
C. 1.999
D. 2.000
E. 2.001
16 Sep 2014, 01:20
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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
The answer options are extremely close to each other, necessitating a very precise calculation. We can't simply round off 2.001 to 2 and assert that \(\frac{4}{2.001}\) is closest to 2 from the options given, due to this small difference.
Let's express 2.001 as 2 + 0.001 and multiply both the numerator and the denominator by the conjugate, 2 - 0.001:
\(\frac{4}{2.001}=\)
\(=\frac{4}{2+0.001}=\)
\(=\frac{4(2-0.001)}{(2+0.001)(2-0.001)}=\)
\(=\frac{4(2-0.001)}{4-0.001^2}\).
Now, \(0.001^2=0.000001\) is a very small number. Compared to 4, this value is practically negligible (do note that while we couldn't ignore 0.001 earlier, we can overlook 0.000001 now because it is 1000 times smaller than 0.001). Hence, we can approximate the equation as:
\(\frac{4(2-0.001)}{4-0.001^2} \approx \)
\(\approx \frac{4(2-0.001)}{4}=\)
\(= 2-0.001 =\)
\(=1.999\).
Therefore, \(\frac{4}{2.001}\) is closest to 1.999 among the provided options.
Answer: C
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
The answer options are extremely close to each other, necessitating a very precise calculation. We can't simply round off 2.001 to 2 and assert that \(\frac{4}{2.001}\) is closest to 2 from the options given, due to this small difference.
Let's express 2.001 as 2 + 0.001 and multiply both the numerator and the denominator by the conjugate, 2 - 0.001:
\(\frac{4}{2.001}=\)
\(=\frac{4}{2+0.001}=\)
\(=\frac{4(2-0.001)}{(2+0.001)(2-0.001)}=\)
\(=\frac{4(2-0.001)}{4-0.001^2}\).
Now, \(0.001^2=0.000001\) is a very small number. Compared to 4, this value is practically negligible (do note that while we couldn't ignore 0.001 earlier, we can overlook 0.000001 now because it is 1000 times smaller than 0.001). Hence, we can approximate the equation as:
\(\frac{4(2-0.001)}{4-0.001^2} \approx \)
\(\approx \frac{4(2-0.001)}{4}=\)
\(= 2-0.001 =\)
\(=1.999\).
Therefore, \(\frac{4}{2.001}\) is closest to 1.999 among the provided options.
Answer: C
General Discussion
Ralphcuisak
Joined: 07 Mar 2013
Last visit: 04 Jun 2016
Posts: 270
Given Kudos: 444
Status:The Final Countdown
Concentration: Technology, General Management
Schools: Goizueta '18 (D) Kelley '18 (WL) Scheller '18 (A) W. P. Carey Arizona State '18 (A) Olin '18 (A$) Mendoza '18 (A) Tippie '18 (A) Smeal Penn'18 (A)
GMAT 1: 710 Q47 V41
GPA: 3.84
WE:Information Technology (Computer Software)
Schools: Goizueta '18 (D) Kelley '18 (WL) Scheller '18 (A) W. P. Carey Arizona State '18 (A) Olin '18 (A$) Mendoza '18 (A) Tippie '18 (A) Smeal Penn'18 (A)
GMAT 1: 710 Q47 V41
Posts: 270
21 Jul 2015, 03:57
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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?
