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(11+1/11
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18 Feb 2021, 04:22
18 Feb 2021, 04:22
Expert Reply
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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
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: (11+1/11
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18 Feb 2021, 06:11
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
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
Retired Moderator
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Status:Founder & Quant Trainer
Affiliations: Prepster Education
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Location: India
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(11+1/11
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18 Feb 2021, 06:45
18 Feb 2021, 06:45
1
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. 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
