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(3.999999 / 2.001) - (3.999996 / 2.002)

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(3.999999 / 2.001) - (3.999996 / 2.002)  [#permalink]

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New post 02 Aug 2019, 21:58
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

54% (02:10) correct 46% (02:01) wrong based on 48 sessions

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\(\frac{(3.999999)}{(2.001)} - \frac{(3.999996)}{(2.002)} = ?\)\(\)

A) \(\frac{(1)}{(1000)}\)
B) \(\frac{(1)}{(10000)}\)
C) \(\frac{(1)}{(100000)}\)
D) \(\frac{(1)}{(1000000)}\)
E) \(\frac{(1)}{(10000000)}\)
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(3.999999 / 2.001) - (3.999996 / 2.002)  [#permalink]

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New post 02 Aug 2019, 22:39
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Simplify as below


\(\frac{(4- 10^{-6})}{(2+10^{-3})}-\frac{(4- 4*10^{-6})}{(2+ 2*10^{-3})}\)

We know that \((4- 10^{-6}) = (2+10^{-3})*(2-10^{-3})\)

Hence our expression becomes

=\((2-10^{-3})- (2-2*10^{-3})\)
=\(1.999-1.998\)
=\(0.001\)
=\(\frac{1}{1000}\)

Hence, A
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(3.999999 / 2.001) - (3.999996 / 2.002)  [#permalink]

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New post Updated on: 02 Aug 2019, 22:31
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(4-\(\frac{1}{10^6}\))/(2-\(\frac{1}{10^3}\)) - (4-\(\frac{4}{10^6}\))/(2+\(\frac{2}{10^3}\))=
---------------------------------------------------------------------------------------------------------------------------------------
(2-\(\frac{1}{10^3}\))(2+\(\frac{1}{10^3}\))/(2+\(\frac{1}{10^3}\))-(2-\(\frac{2}{10^3}\))(2+\(\frac{2}{10^3}\))/(2+\(\frac{2}{10^3}\))=
---------------------------------------------------------------------------------------------------------------------------------------
(2-\(\frac{1}{10^3}\))-(2-\(\frac{2}{10^3}\))=2-\(\frac{1}{10^3}\)-2+\(\frac{2}{10^3}\)=\(\frac{1}{10^3}\)=\(\frac{1}{1000}\)

The answer choice A.

Originally posted by lacktutor on 02 Aug 2019, 22:23.
Last edited by lacktutor on 02 Aug 2019, 22:31, edited 5 times in total.
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Re: (3.999999 / 2.001) - (3.999996 / 2.002)  [#permalink]

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New post 02 Aug 2019, 22:24
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Cant be expected to solve this by division so should look to simplify the expression.

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Re: (3.999999 / 2.001) - (3.999996 / 2.002)  [#permalink]

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New post 12 Aug 2019, 13:00
1
hamed288 wrote:
\(\frac{(3.999999)}{(2.001)} - \frac{(3.999996)}{(2.002)} = ?\)\(\)

A) \(\frac{(1)}{(1000)}\)
B) \(\frac{(1)}{(10000)}\)
C) \(\frac{(1)}{(100000)}\)
D) \(\frac{(1)}{(1000000)}\)
E) \(\frac{(1)}{(10000000)}\)


Or you can just look at the fact that you are dealing with 6 decimal places divided by 3 decimal places resulting in 3 decimal places. Option A.
Does it make sense or I am just randomly guessing it?
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Re: (3.999999 / 2.001) - (3.999996 / 2.002)   [#permalink] 12 Aug 2019, 13:00
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