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(11+1/11

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Carcass
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(11+1/11 [#permalink] New post   18 Feb 2021, 04:22
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Question Stats:

86% (01:12) correct 13% (01:58) wrong based on 44 sessions

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\((11+\frac{1}{11})^2-(11-\frac{1}{11})^2=?\)

A. 2
B. 3
C. 4
D. 5
E. 9


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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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C
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Re: (11+1/11 [#permalink] New post   18 Feb 2021, 06:11
1
Carcass wrote:
\((11+\frac{1}{11})^2-(11-\frac{1}{11})^2=?\)

A. 2
B. 3
C. 4
D. 5
E. 9


Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book

Key concept: \(x^2 - y^2\) is called a difference of squares, which can be factored as follows: \(x^2 - y^2= (x+y)(x-y)\)

So....
\((11+\frac{1}{11})^2-(11-\frac{1}{11})^2=[(11+\frac{1}{11})+(11-\frac{1}{11})][(11+\frac{1}{11})-(11-\frac{1}{11})]\)

\(=[22][\frac{2}{11}]\)

\(=\frac{44}{11}\)

\(= 4\)

Answer: C
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(11+1/11 [#permalink] New post   18 Feb 2021, 06:45
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Carcass wrote:
\((11+\frac{1}{11})^2-(11-\frac{1}{11})^2=?\)

A. 2
B. 3
C. 4
D. 5
E. 9



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

\((11+\frac{1}{11})^2-(11-\frac{1}{11})^2=?\)

= \((11+\frac{1}{11}+11-\frac{1}{11})(11+\frac{1}{11}-11+\frac{1}{11})\)

= \((11+11)(\frac{1}{11}+\frac{1}{11})\)

= \((22)(\frac{2}{11})\)

= \(4\)

Hence, option C
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(11+1/11 [#permalink] New post   18 Feb 2021, 06:59
1
Hi,

You can also do this using calculator.

1/11=0.0909
11+0.09090=(11.9090)^2~123
11-0.90909=(10.09091)^2~119

Thus, 123-119=4

IMO C

Hope this helps!
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18 Feb 2021, 06:59
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