2² - 4² + 6² - 8² + 10² - 12² + 14² - 16² + 18² - 20² =
A) -40
B) -110
C) -220
D) -440
E) -880
Answer: C
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Difficulty level: 650 -700
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Somewhat tricky calculation: 2² - 4² + 6² - 8² + ...
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Brent@GMATPrepNow
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DavidG@VeritasPrep
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Fun one. If we group the terms into pairs, a pattern emerges: 2² - 4² = -12; 6² - 8² = -28; 10² - 12² = -44Brent@GMATPrepNow wrote:2² - 4² + 6² - 8² + 10² - 12² + 14² - 16² + 18² - 20² =
A) -40
B) -110
C) -220
D) -440
E) -880
Answer: C
Source: www.gmatprepnow.com
Difficulty level: 650 -700
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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DavidG@VeritasPrep
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Time Saver:
In an evenly spaced set, the mean = median = (high + low)/2
First term = -12
Last term = -76
Mean (average) = (-12+-76)/2 = -44
There are 5 terms.
Average * # terms = (-44) * 5 = -220
In an evenly spaced set, the mean = median = (high + low)/2
First term = -12
Last term = -76
Mean (average) = (-12+-76)/2 = -44
There are 5 terms.
Average * # terms = (-44) * 5 = -220
GMAT/MBA Expert
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Brent@GMATPrepNow
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Another approach:Brent@GMATPrepNow wrote:2² - 4² + 6² - 8² + 10² - 12² + 14² - 16² + 18² - 20² =
A) -40
B) -110
C) -220
D) -440
E) -880
Answer: C
Source: www.gmatprepnow.com
Difficulty level: 650 -700
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)
= [spoiler]-220
[/spoiler]
Answer: C
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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DavidG@VeritasPrep
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Nice difference of squares action there. Elegant solution, Brent.Brent@GMATPrepNow wrote:Another approach:Brent@GMATPrepNow wrote:2² - 4² + 6² - 8² + 10² - 12² + 14² - 16² + 18² - 20² =
A) -40
B) -110
C) -220
D) -440
E) -880
Answer: C
Source: www.gmatprepnow.com
Difficulty level: 650 -700
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)
= [spoiler]-220
[/spoiler]
Answer: C
Cheers,
Brent
