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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8023
GMAT 1: 760 Q51 V42 GPA: 3.82

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Difficulty:   25% (medium)

Question Stats: 80% (01:43) correct 20% (02:03) wrong based on 221 sessions

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(1+√3+√5)^2-(√3+√5)^2=?
A. 1+2√3+2√5
B. 1+2√3+3√5
C. 1-√3+√5
D. 1+√3-√5
E. √3+√5

*An answer will be posted in 2 days.

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Joined: 12 Sep 2015
Posts: 4015

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(1+√3+√5)² - (√3+√5)² = ?

A. 1+2√3+2√5
B. 1+2√3+3√5
C. 1-√3+√5
D. 1+√3-√5
E. √3+√5

Nice question!
First recognize that (1+√3+√5)² - (√3+√5)² is a DIFFERENCE OF SQUARES.
Here are some examples of differences of squares:
x² - 25y²
4x² - 9y²
49m² - 100k²

In general, we can factor differences of squares as follows:
- = (a+b)(a-b)

So, (1+√3+√5)² - (√3+√5)² = [(1+√3+√5) + (√3+√5)][(1+√3+√5) - (√3+√5)]
= [1+2√3+2√5]
= 1+2√3+2√5

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Originally posted by GMATPrepNow on 26 Jun 2016, 12:42.
Last edited by GMATPrepNow on 16 Oct 2018, 07:54, edited 1 time in total.
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Current Student Joined: 18 Oct 2014
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Location: United States
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(1+√3+√5)^2-(√3+√5)^2

(1+√3)^2 + 5 +2 (1+√3) (√5) - ( 3 +5 + 2√3√5)

1+ 3+ 2√3 +5 +2 √5 + 2 √15 - 3-5 -2√15

1+2√3+2√5

A is the answer
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8023
GMAT 1: 760 Q51 V42 GPA: 3.82

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A^2-B^2=(A+B)(A-B). Hence, the correct answer is A.
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MathRevolution wrote:
(1+√3+√5)^2-(√3+√5)^2=?
A. 1+2√3+2√5
B. 1+2√3+3√5
C. 1-√3+√5
D. 1+√3-√5
E. √3+√5

*An answer will be posted in 2 days.

you can even do it with (A+B)^2 formula:

let √3+√5=x
Then the question becomes:
(1+x)^2-(x)^2=1^2+x^2+2x-x^2=1+2x=1+2(√3+√5)= option B
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GMAT Club Legend  V
Joined: 12 Sep 2015
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MathRevolution wrote:
(1+√3+√5)^2 - (√3+√5)^2=?
A. 1+2√3+2√5
B. 1+2√3+3√5
C. 1-√3+√5
D. 1+√3-√5
E. √3+√5

Another approach:

For test day, everyone should know the following approximations:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2

So, (1+√3+√5)² - (√3+√5)² ≈ (1+ 1.7 + 2.2)² - (1.7 + 2.2)²
≈ (4.9)² - (3.9)²
≈ 25 - 16
9

Now check the answer choices....
A. 1+2√3+2√5 ≈ 1 + 2(1.7) + 2(2.2) ≈ 8.8. CLOSE - KEEP
B. 1+2√3+3√5 ≈ 1 + 2(1.7) + 3(2.2) ≈ 11. ELIMINATE
C. 1-√3+√5 ≈ 1 - 1.7 + 2.2 ≈ 1.5. ELIMINATE
D. 1+√3-√5 ≈1 + 1.7 - 2.2 ≈ 0.4. ELIMINATE
E. √3+√5 ≈ 1.7 + 2.2 ≈ 3.9. ELIMINATE

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_________________ Re: (1+√3+√5)^2-(√3+√5)^2=?   [#permalink] 24 Oct 2018, 00:25
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