-Patrick
This takes too long!!! Shortcuts?
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Source: Beat The GMAT — Problem Solving |
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Patrick_GMATFix
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You're right, you're not supposed to actually calculate through brute force! This is a test of the common quadratic x^2 - y^2 = (x-y)(x+y). The answer is A. I go through the question in detail in the full solution below (taken from the GMATFix App).
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GMATGuruNY
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Always be on the lookout for the following quadratic identities:kobel51 wrote:(sqr(2)+1)*(sqr(2)-1)*(sqr(3)+1)*(sqr(3)-1) =
A) 2
B) 3
C) 2*sqr(6)
D) 5
E) 6
I thought about estimating but seems like there should be a faster way
(a+b)² = a² + 2ab + b²
(a-b)² = a² - 2ab + b²
(a+b)(a-b) = a² - b².
The problem above is testing our ability to recognize the bottom identity, known as the DIFFERENCE OF TWO SQUARES:
(√2 + 1)(√2 - 1) * (√3 + 1)(√3 - 1)
= [ (√2)² - 1² ] * [ (√3)² - 1² ]
= (2-1)(3-1)
= 1*2
= 2.
The correct answer is A.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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theCodeToGMAT
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[(sqrt(2) + 1 ) (sqrt(2) - 1)] * [ (sqrt(3) + 1) (sqrt(3) - 1) ]
using formula (a+b)(a-b) = a^2 - b^2
= (2-1) * (3-1)
= 2
[spoiler]{A}[/spoiler]
using formula (a+b)(a-b) = a^2 - b^2
= (2-1) * (3-1)
= 2
[spoiler]{A}[/spoiler]
R A H U L
