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Let S denote the sum of the squares of ten consecutive positive

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Joined: 18 Jul 2019
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Let S denote the sum of the squares of ten consecutive positive  [#permalink]

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New post 25 Nov 2019, 03:54
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Difficulty:

  95% (hard)

Question Stats:

10% (02:19) correct 90% (02:14) wrong based on 21 sessions

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Let S denote the sum of the squares of ten consecutive positive integers. Which of the following values represents a possible value of S?

(A) 2485
(B) 2585
(C) 2685
(D) 2785
(E) 2895
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Joined: 02 Aug 2009
Posts: 8284
Re: Let S denote the sum of the squares of ten consecutive positive  [#permalink]

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New post 25 Nov 2019, 06:15
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CaptainLevi wrote:
Let S denote the sum of the squares of ten consecutive positive integers. Which of the following values represents a possible value of S?

(A) 2485
(B) 2585
(C) 2685
(D) 2785
(E) 2895


\(S=(a-5)^2+(a-4)^2+(a-3)^2+(a-2)^2+(a-1)^2+a^2+(a+1)^2+(a+2)^2+(a+3)^2+(a+4)^2\)
=\((a-5)^2+(a-4)^2+(a+4)^2+...=a^2-10a+25+2(a^2+4^2)+2(a^2+3^2)..+2(a^2).\)
=\(a^2-10a+25+a^2+2(4a^2+1^2+2^2+3^2+4^2)=a^2-10a+25+a^2+2(4a^2+1+4+9+16)\)
=\(10a^2-10a+25+60=10a(a-1)+85\)

Check the choices..

(A) 2485......10a(a-1)+85=2485......10a(a-1)=2400......a(a-1)=240=15*16...Possible
(B) 2585......10a(a-1)+85=2585......10a(a-1)=2500......a(a-1)=250=2*5^3...Not Possible
Similarly for other choices

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Re: Let S denote the sum of the squares of ten consecutive positive  [#permalink]

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New post 30 Nov 2019, 21:58
CaptainLevi wrote:
Let S denote the sum of the squares of ten consecutive positive integers. Which of the following values represents a possible value of S?

(A) 2485
(B) 2585
(C) 2685
(D) 2785
(E) 2895



Could you please share the solution?
GMAT Club Bot
Re: Let S denote the sum of the squares of ten consecutive positive   [#permalink] 30 Nov 2019, 21:58
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Let S denote the sum of the squares of ten consecutive positive

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