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## Somewhat tricky calculation: 2Â² - 4Â² + 6Â² - 8Â² + ...

tagged by: Brent@GMATPrepNow

This topic has 4 expert replies and 0 member replies

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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#### Somewhat tricky calculation: 2Â² - 4Â² + 6Â² - 8Â² + ...

Tue May 02, 2017 5:46 am
2Â² - 4Â² + 6Â² - 8Â² + 10Â² - 12Â² + 14Â² - 16Â² + 18Â² - 20Â² =

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

Source: www.gmatprepnow.com
Difficulty level: 650 -700

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DavidG@VeritasPrep Legendary Member
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Tue May 02, 2017 6:37 am
Brent@GMATPrepNow wrote:
2Â² - 4Â² + 6Â² - 8Â² + 10Â² - 12Â² + 14Â² - 16Â² + 18Â² - 20Â² =

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

Source: www.gmatprepnow.com
Difficulty level: 650 -700
Fun one. If we group the terms into pairs, a pattern emerges: 2Â² - 4Â² = -12; 6Â² - 8Â² = -28; 10Â² - 12Â² = -44
Each successive term is 16 less than the previous term. We'll have 5 pairs, so 5 terms: -12, -28, -44, -60, -76. We could just add them here and get -220 or C

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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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Tue May 02, 2017 10:38 am
Brent@GMATPrepNow wrote:
2Â² - 4Â² + 6Â² - 8Â² + 10Â² - 12Â² + 14Â² - 16Â² + 18Â² - 20Â² =

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

Source: www.gmatprepnow.com
Difficulty level: 650 -700
Another approach:

2Â² - 4Â² + 6Â² - 8Â² + 10Â² - 12Â² + 14Â² - 16Â² + 18Â² - 20Â² = (2Â² - 4Â²) + (6Â² - 8Â²) + (10Â² - 12Â²) + (14Â² - 16Â²) + (18Â² - 20Â²)
= (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

Cheers,
Brent

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DavidG@VeritasPrep Legendary Member
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Wed May 03, 2017 8:38 am
Brent@GMATPrepNow wrote:
Brent@GMATPrepNow wrote:
2Â² - 4Â² + 6Â² - 8Â² + 10Â² - 12Â² + 14Â² - 16Â² + 18Â² - 20Â² =

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

Source: www.gmatprepnow.com
Difficulty level: 650 -700
Another approach:

2Â² - 4Â² + 6Â² - 8Â² + 10Â² - 12Â² + 14Â² - 16Â² + 18Â² - 20Â² = (2Â² - 4Â²) + (6Â² - 8Â²) + (10Â² - 12Â²) + (14Â² - 16Â²) + (18Â² - 20Â²)
= (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

Cheers,
Brent
Nice difference of squares action there. Elegant solution, Brent.

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