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# 2^2 - 4^2 + 6^2 - 8^2 + 10^2 - 12^2 + 14^2 - 16^2 + 18^2

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GRE Instructor
Joined: 10 Apr 2015
Posts: 581
Followers: 27

Kudos [?]: 370 [1] , given: 1

2^2 - 4^2 + 6^2 - 8^2 + 10^2 - 12^2 + 14^2 - 16^2 + 18^2 [#permalink]  06 Jun 2017, 13:08
1
KUDOS
Expert's post
00:00

Difficulty:

5% (low)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
2^2 - 4^2 + 6^2 - 8^2 + 10^2 - 12^2 + 14^2 - 16^2 + 18^2 - 20^2 =

A) -40
B) -110
C) -220
D) -440
E) -880
[Reveal] Spoiler: OA

_________________

Brent Hanneson – Founder of greenlighttestprep.com

Check out the online reviews of our course

GRE Instructor
Joined: 10 Apr 2015
Posts: 581
Followers: 27

Kudos [?]: 370 [1] , given: 1

Re: 2^2 - 4^2 + 6^2 - 8^2 + 10^2 - 12^2 + 14^2 - 16^2 + 18^2 [#permalink]  07 Jun 2017, 15:06
1
KUDOS
Expert's post
GreenlightTestPrep wrote:
2^2 - 4^2 + 6^2 - 8^2 + 10^2 - 12^2 + 14^2 - 16^2 + 18^2 - 20^2 =

A) -40
B) -110
C) -220
D) -440
E) -880

Here's an approach that uses differences of squares

2² - 4² + 6² - 8² + 10² - 12² + 14² - 16² + 18² - 20² = (2² - 4²) + (6² - 8²) + (10² - 12²) + (14² - 16²) + (18² - 20²)
= (2 - 4)(2 + 4) + (6 - 8)(6 + 8) + (10 - 12)(10 + 12) + (14 - 16)(14 + 16) + (18 - 20)(18 + 20)
= (-2)(2 + 4) + (-2)(6 + 8) + (-2)(10 + 12) + (-2)(14 + 16) + (-2)(18 + 20)
= -2(2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20)
= -2(2)(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)
= (-4)(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)
= (-4)(55)
= -220

[Reveal] Spoiler:
C

Cheers,
Brent
_________________

Brent Hanneson – Founder of greenlighttestprep.com

Check out the online reviews of our course

Re: 2^2 - 4^2 + 6^2 - 8^2 + 10^2 - 12^2 + 14^2 - 16^2 + 18^2   [#permalink] 07 Jun 2017, 15:06
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