((0.9996/0.98) - 1) =

Question

((\frac{0.9996}{0.98}) - 1) = (A) \frac{1}{50} (B) \frac{1}{98} (C) \frac{2}{49} (D) \frac{3}{49} (E) \frac{3}{196} For an elegant no-calculator explanation to this problem, as well as a bank of nine other problems on fractions & decimals, see: https://magoosh.com/gmat/2014/gmat-pract ... -decimals/ Mike :-)

PareshGmat · Accepted Answer

\frac{0.9996}{0.98} - 1 = \frac{0.9996-0.9800}{0.98} = \frac{0.0196}{0.98} = \frac{196}{9800} = \frac{2}{100} = \frac{1}{50}

Answer = A

manpreetsingh86 · Answer

{9996 x10^(-4)/98x10^(-2) } - 1

= 1.02-1 = .02
=2/100
=1/50

WoundedTiger · Answer

((\frac{0.9996}{0.98}) - 1) =

Can be re-written as ((\frac{(0.9800+0.0196)}{0.9800} )-1)

((1+0.02)-1)  or 0.02 or 2/100 ----1/50

Ans is A

annasejahat · Answer

This is how i see it

0.0096 = 1-0.0004 = 1-4(10)^-4 and 0.98 = 1 - 2(10)^-2

remember a2-b2 = (a-b) x (a-b)

so 1-4(10)^-4 / 1 - 2(10)^-2 is now (1 - 2(10)^-2) x (1 + 2(10)^-2) divided with 1 - 2(10)^-2

so u get (1 + 2(10)^-2) -1 = 0.02 = 2/100 = 1/50

pacifist85 · Answer

I probably didn't use a really smart way, but here it is:

0.9996/0.98 - 1 = 0.9996 - 0.98 / 0.98 = 0.196 / 0.98 = (multiply both by 1000) = 196 / 9800 = 1 / 50.  ANS A

* here: 0.9996 - 0.98 / 0.98, I just turned the 2 fractions into having the same denominator (I don't remember the name of this process - let's say LCM).

bv8562 · Answer

((\frac{0.9998}{0.98})-1)  =  ((\frac{1-0.0004}{1-0.02})-1)  =  ((\frac{1-2^{2}*10^{-4}}{1-2*10^{-2}})-1)  =  ((\frac{(1)^{2}-(2*10^{-2})^{2}}{1-2*10^{-2}})-1)

=  ((\frac{(1-2*10^{-2})(1+2*10^{-2})}{(1-2*10^{-2})})-1)  =  (1+0.02-1)  =  0.02  =  \frac{2}{100}  =  \frac{1}{50}   (A)

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((0.9996/0.98) - 1) =

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