99,999^2 - 1^2 = : GMAT Problem Solving (PS)
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# 99,999^2 - 1^2 =

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11 Feb 2013, 07:34
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Difficulty:

35% (medium)

Question Stats:

71% (01:53) correct 29% (01:36) wrong based on 176 sessions

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99,999^2 - 1^2 =

A. 10^10 - 2
B. (10^5 – 2)^2
C. 10^4(10^5 – 2)
D. 10^5(10^4 – 2)
E. 10^5(10^5 – 2)
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Feb 2013, 07:38, edited 1 time in total.
Renamed the topic and edited the question.
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Re: 99,999^2 - 1^2 = [#permalink]

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11 Feb 2013, 07:39
4112019 wrote:
99,999^2 - 1^2 =

A. 10^10 - 2
B. (10^5 – 2)^2
C. 10^4(10^5 – 2)
D. 10^5(10^4 – 2)
E. 10^5(10^5 – 2)

99,999^2 - 1^2 =

A. 10^10 - 2
B. (10^5 – 2)^2
C. 10^4(10^5 – 2)
D. 10^5(10^4 – 2)
E. 10^5(10^5 – 2)

Apply $$a^2-b^2=(a+b)(a-b)$$:

$$99,999^2-1^2 =(99,999+1)(99,999-1)=10^5(10^5-1-1)=10^5(10^5-2)$$

Hope it's clear.
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Re: 99,999^2 - 1^2 = [#permalink]

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13 Mar 2015, 02:44
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Re: 99,999^2 - 1^2 = [#permalink]

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09 Jul 2016, 03:20
(99,999)^2 - (1)^2 = (100,000 -1)^2 - (1)^2 = (100,000)^2 - 2*100,000 + 1-1=(10^5)^2 - 2*(10^5) = 10^10 - 2*(10^5)=10^5(10^5 - 2) Answer E
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Re: 99,999^2 - 1^2 = [#permalink]

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09 Jul 2016, 08:10
1
KUDOS
4112019 wrote:
99,999^2 - 1^2 =

A. 10^10 - 2
B. (10^5 – 2)^2
C. 10^4(10^5 – 2)
D. 10^5(10^4 – 2)
E. 10^5(10^5 – 2)

99,999^2 - 1^2

a^2-b^2= (a+b) (a-b)

(99,999+1) (99,999-1)
10^5 (99,998)

10^5 (10^5-2)
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Re: 99,999^2 - 1^2 =   [#permalink] 09 Jul 2016, 08:10
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