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Intern  B
Joined: 16 Jul 2019
Posts: 3
(3.999999 / 2.001) - (3.999996 / 2.002)  [#permalink]

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1
6 00:00

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) $$\frac{(1)}{(10000000)}$$
##### Most Helpful Community Reply
Senior Manager  P
Joined: 05 Jul 2018
Posts: 350
Location: India
Concentration: General Management, Technology
GMAT 1: 600 Q47 V26 GRE 1: Q162 V149 GPA: 3.6
WE: Information Technology (Consulting)
(3.999999 / 2.001) - (3.999996 / 2.002)  [#permalink]

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5
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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##### General Discussion
Manager  S
Joined: 25 Jul 2018
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(3.999999 / 2.001) - (3.999996 / 2.002)  [#permalink]

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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.
Intern  B
Joined: 02 Jun 2014
Posts: 49
Schools: ISB '15
Re: (3.999999 / 2.001) - (3.999996 / 2.002)  [#permalink]

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3
1
A

Cant be expected to solve this by division so should look to simplify the expression.

Pfa solutions

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Manager  S
Joined: 18 Dec 2017
Posts: 176
Re: (3.999999 / 2.001) - (3.999996 / 2.002)  [#permalink]

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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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Software Tester currently in USA ( ) Re: (3.999999 / 2.001) - (3.999996 / 2.002)   [#permalink] 12 Aug 2019, 13:00
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