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# (1.0004)(0.9998) – (1.0002)(0.9996) =

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Director
Joined: 12 Feb 2015
Posts: 917

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Updated on: 01 Jul 2018, 00:34
3
4
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Difficulty:

55% (hard)

Question Stats:

60% (02:08) correct 40% (01:55) wrong based on 111 sessions

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(1.0004)(0.9998) – (1.0002)(0.9996) =

(A) 0.00000002
(B) 0.00000004
(C) 0.00000008
(D) 0.0004
(E) 0.0002

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Manish

"Only I can change my life. No one can do it for me"

Originally posted by CAMANISHPARMAR on 16 Jun 2018, 09:55.
Last edited by CAMANISHPARMAR on 01 Jul 2018, 00:34, edited 1 time in total.
Director
Joined: 12 Feb 2015
Posts: 917
Re: (1.0004)(0.9998) – (1.0002)(0.9996) =  [#permalink]

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Updated on: 01 Jul 2018, 00:33
5
Let x = 0.0002.

Therefore (1.0004)(0.9998) – (1.0002)(0.9996) can be written as:-

= (1 + 2x)(1 – x) – (1 + x)(1 – 2x) = 2x [On simplification]

Substitute x = 0.0002 in 2x

Therefore 2(0.0002) = 0.0004.

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Manish

"Only I can change my life. No one can do it for me"

Originally posted by CAMANISHPARMAR on 16 Jun 2018, 10:02.
Last edited by CAMANISHPARMAR on 01 Jul 2018, 00:33, edited 1 time in total.
##### General Discussion
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Re: (1.0004)(0.9998) – (1.0002)(0.9996) =  [#permalink]

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16 Jun 2018, 11:56
1
CAMANISHPARMAR wrote:
(1.0004)(0.9998) – (1.0002)(0.9996) =

A. 0.00000002
B. 0.00000004
C. 0.00000008
D. 0.0004
E. 0.0002

(1.0004)(0.9998) is of form $$(a + b)(a - b) = (a^2 - b^2)$$ where a = 1.0001 and b = 0.0003
(1.0002)(0.9996) is of form $$(a + b)(a - b) = (a^2 - b^2)$$ where a = 0.9999 and b = 0.0003

$$(1.0004)(0.9998) – (1.0002)(0.9996) = (1.0001)^2-(0.0003)^2-(0.9999)^2+(0.0003)^2 = (1.0001)^2 - (0.9999)^2 = 2(0.0002)$$

Therefore, the value of the expression is 0.0004(Option D)
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Joined: 18 Jul 2017
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Re: (1.0004)(0.9998) – (1.0002)(0.9996) =  [#permalink]

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19 Jun 2018, 17:24
pushpitkc

I didn't understand how did you get this?

(1.0001)2−(0.9999)2=2(0.0002)
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Joined: 02 Aug 2009
Posts: 7960
Re: (1.0004)(0.9998) – (1.0002)(0.9996) =  [#permalink]

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19 Jun 2018, 19:58
wishalsp333 wrote:
pushpitkc

I didn't understand how did you get this?

(1.0001)2−(0.9999)2=2(0.0002)

Hi...
$$(1.0004)(0.9998)-(1.0002)(0.9996)=(1.0001+0.0003)(1.0001-0.0003)-(0.9999+0.0003)(0.9999-0.0003)=$$

$$(1.0001^2-0.0003^2)-(0.9999^2-0.0003^2)...$$

$$=> 1.0001^2-0.0003^2-0.9999^2+0.0003^2=1.0001^2-0.9999^2=(1.0001-0.9999)(1.0001+0.9999)=0.0002*2=0.0004$$
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Re: (1.0004)(0.9998) – (1.0002)(0.9996) =   [#permalink] 19 Jun 2018, 19:58
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