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99,999^2 - 1^2 =

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4112019
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99,999^2 - 1^2 = [#permalink] New post  Updated on: 19 Sep 2018, 23:30
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70% (01:31) correct 30% (01:53) wrong based on 503 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. \(10^5(10^5 – 2)\)
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Originally posted by 4112019 on 11 Feb 2013, 08:34.
Last edited by Bunuel on 19 Sep 2018, 23:30, edited 2 times in total.
Renamed the topic and edited the question.
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Bunuel
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Re: 99,999^2 - 1^2 = [#permalink] New post  11 Feb 2013, 08:39
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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 \(a^2-b^2=(a+b)(a-b)\):

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

Answer: E.

Hope it's clear.
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Re: 99,999^2 - 1^2 = [#permalink] New post  09 Jul 2016, 09:10
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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)
E is the answer
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Re: 99,999^2 - 1^2 = [#permalink] New post  09 Jul 2016, 04:20
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(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] New post  08 May 2018, 11:23
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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)


Using the difference of squares, we have:

(99,999 + 1)(99,999 - 1)

(100,000)(99,998)

(100,000)(100,000 - 2)

10^5(10^5 - 2)

Answer: E
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Re: 99,999^2 - 1^2 = [#permalink] New post  21 May 2018, 06:11
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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 =

(99999 - 1) (99999 + 1)

99998 * 100000

(10^5 - 2) * 10^5

Hence (E)
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Re: 99,999^2 - 1^2 = [#permalink] New post  21 May 2018, 08:32
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)


\(99,999^2 - 1^2\) \(=\) \((99,999 - 1)(99,999 + 1)\)

Or, \(99,999^2 - 1^2\) \(=\) \(99,99800000\)

Or, \(99,999^2 - 1^2\) \(=\) \(100,00000000 - 200000\)

Or, \(99,999^2 - 1^2\) \(=\) \(10^5(10^5 – 2)\), Answer must be (E)
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Re: 99,999^2 - 1^2 = [#permalink] New post  21 May 2018, 22:32
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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)

Ans: E
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Re: 99,999^2 - 1^2 = [#permalink] New post  25 Oct 2020, 06:29
Difference of squares = \(a^2 - b^2 = (a+b)(a-b)\)

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

Answer is. E
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Re: 99,999^2 - 1^2 = [#permalink] New post  08 Apr 2024, 09:04
Expert Reply
 
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. \(10^5(10^5 – 2)\)

­
You can also use (a-b)^2 here. 

\(99,999^2 - 1^2\\
= (10^5 - 1)^2 - 1^2\\
= 10^{10} - 2*10^5 + 1 - 1^2\\
= 10^{10} - 2*10^5\\
= 10^5(10^5 - 2)\)­

Answer (E)­
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Re: 99,999^2 - 1^2 = [#permalink]
08 Apr 2024, 09:04
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