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((0.9996/0.98) - 1) =

by Mike@Magoosh » Mon Jun 09, 2014 12:03 pm
((0.9996/0.98) - 1) =
(A) 1/50
(B) 1/98
(C) 2/49
(D) 3/49
(E) 3/196

For the answer and elegant no-calculator solution to this problem, as well as nine other problems with fractions & decimals, see:
https://magoosh.com/gmat/2014/gmat-pract ... -decimals/

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by Mathsbuddy » Fri Jun 13, 2014 9:02 am
0.9996 - 0.98 = 0.98p
so p = 0.0196 = approx 0.02 = 1/50
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by GMATinsight » Fri Jun 13, 2014 9:29 am
((0.9996/0.98) - 1) = [(1-0.0004)/0.98]-1 = [(1^2-0.02^2)/0.98]-1
= [(1+0.02)*(1-0.02)/(1-0.02)]-1
= (1+0.02)-1 = 0.02 = 2/100 = 1/50 Answer
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by GMATGuruNY » Fri Jun 13, 2014 9:40 am
Mike@Magoosh wrote:((0.9996/0.98) - 1) =
(A) 1/50
(B) 1/98
(C) 2/49
(D) 3/49
(E) 3/196

For the answer and elegant no-calculator solution to this problem, as well as nine other problems with fractions & decimals, see:
https://magoosh.com/gmat/2014/gmat-pract ... -decimals/

Mike :-)
Alternate approach:

(0.9996/0.98) - 1

= 9996/9800 - 9800/9800

= 196/9800

= (98*2)/(98*100)

= 2/100

= 1/50.

The correct answer is A.
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by Brent@GMATPrepNow » Fri Jun 13, 2014 11:05 am
Mike@Magoosh wrote:((0.9996/0.98) - 1) =
(A) 1/50
(B) 1/98
(C) 2/49
(D) 3/49
(E) 3/196
This approach is similar to Mitch's with an ESTIMATION twist at the end:

0.9996/0.98 - 1 = 0.9996/0.98 - 0.98/0.98 [rewrote with common denominator of 0.98]
= 9996/9800 - 9800/9800 [multiplied top and bottom of each fraction by 10,000 to make easier to work with]
= (9996 - 9800)/9800
= 196/9800
IMPORTANT: Upon checking the answer choices, we can see that the answer choices are well spread apart. So...
196/9800 ≈ 200/10,000
= [spoiler]1/50 = A[/spoiler]

Cheers,
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