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# The formula for the sum of squares of integer between 1 and n is n(

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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The formula for the sum of squares of integer between 1 and n is n( [#permalink]

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24 Sep 2017, 23:52
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25% (medium)

Question Stats:

78% (01:32) correct 22% (00:35) wrong based on 32 sessions

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[GMAT math practice question]

The formula for the sum of squares of integer between 1 and n is n(n+1)(2n+1) / 6 = 1^2 + 2^2 + … + n^2. The is the value of 11^2 + 12^2 + … + 20^2?

A. 2470
B. 2475
C. 2480
D. 2485
E. 2490
[Reveal] Spoiler: OA

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Kudos [?]: 3170 [0], given: 0

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The formula for the sum of squares of integer between 1 and n is n( [#permalink]

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25 Sep 2017, 08:50
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MathRevolution wrote:
[GMAT math practice question]

The formula for the sum of squares of integer between 1 and n is n(n+1)(2n+1) / 6 = 1^2 + 2^2 + … + n^2. The is the value of 11^2 + 12^2 + … + 20^2?

A. 2470
B. 2475
C. 2480
D. 2485
E. 2490

Sum of squares from 1 to 20 $$= \frac{20*21*41}{6} = 2870$$ (use the formula given)

Sum of squares from 1 to 10 $$= \frac{10*11*21}{6} = 385$$

Hence sum of squares from 11 to 20 $$=$$ Sum of squares from 1 to 20 $$-$$ sum of squares from 1 to 10 $$= 2870-385 = 2485$$

Option D

Kudos [?]: 317 [1], given: 39

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4485

Kudos [?]: 3170 [0], given: 0

GPA: 3.82
Re: The formula for the sum of squares of integer between 1 and n is n( [#permalink]

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27 Sep 2017, 00:39
=>

11^2 + 12^2 + … + 20^2
= ( 1^2 + 2^2 + … + 20^2 ) – (1^2 + 2^2 + … + 10^2)
= 20∙21∙41/6 - 10∙11∙21/6
= 2870 – 385
= 2485

Ans: D
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Kudos [?]: 3170 [0], given: 0

Re: The formula for the sum of squares of integer between 1 and n is n(   [#permalink] 27 Sep 2017, 00:39
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