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(5+1/5)^2-(5-1/5)^2=?

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Math Revolution GMAT Instructor
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GMAT 1: 760 Q51 V42
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(5+1/5)^2-(5-1/5)^2=?  [#permalink]

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New post 27 Apr 2017, 01:53
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

82% (00:52) correct 18% (01:23) wrong based on 56 sessions

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\((5+\frac{1}{5})^2-(5-\frac{1}{5})^2\)=?

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

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Re: (5+1/5)^2-(5-1/5)^2=?  [#permalink]

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New post 27 Apr 2017, 01:58
1
(a+b)^2 - (a-b)^2 = 4ab
Here ab = 1
------> 4
------->C
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Re: (5+1/5)^2-(5-1/5)^2=?  [#permalink]

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New post 27 Apr 2017, 02:01
(5+1/5)^2−(5−1/5)^2

Using the formula a^2 - b^2 = (a+b)*(a-b)

Above can be written as

(5+1/5+5-1/5)*(5+1/5-5+1/5) = (5+5)*(1/5+1/5) = 10*2/5 = 4

Answer is C
Math Revolution GMAT Instructor
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Re: (5+1/5)^2-(5-1/5)^2=?  [#permalink]

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New post 30 Apr 2017, 18:12
==> Since \(a^2-b^2=(a-b)(a+b)\), you get \((5+\frac{1}{5})^2-(5-\frac{1}{5})^2=[(5+\frac{1}{5})-(5-\frac{1}{5})][(5+\frac{1}{5})+(5-\frac{1}{5})]=(\frac{2}{5})(10)=4\).

The answer is C.
Answer: C
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Re: (5+1/5)^2-(5-1/5)^2=?  [#permalink]

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New post 06 May 2017, 17:25
MathRevolution wrote:
\((5+\frac{1}{5})^2-(5-\frac{1}{5})^2\)=?

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


Let’s simplify the given expression:

(5 + 1/5)^2 - (5 - 1/5)^2

(5 1/5)^2 - (4 4/5)^2

(26/5)^2 - (24/5)^2

(26/5 + 24/5)(26/5 - 24/5)

(50/5)(2/5) = 10 x 2/5 = 4

Answer: C
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Re: (5+1/5)^2-(5-1/5)^2=? &nbs [#permalink] 06 May 2017, 17:25
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