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Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of
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27 Apr 2020, 15:35
27 Apr 2020, 15:35
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Given that \(1^2 + 2^2 + 3^2 + . . . + 10^2 = 385\), what is the value of \(3^2 + 6^2 + 9^2 + . . . + 30^2\) ?
A. 1,155
B. 1,540
C. 1,925
D. 2,310
E. 3,465
PS19941.02
A. 1,155
B. 1,540
C. 1,925
D. 2,310
E. 3,465
PS19941.02
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Joined: 12 Sep 2015
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Location: Canada
Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of
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Updated on: 04 Oct 2023, 02:47
Updated on: 04 Oct 2023, 02:47
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Top Contributor
parkhydel wrote:
Given that \(1^2 + 2^2 + 3^2 + . . . + 10^2 = 385\), what is the value of \(3^2 + 6^2 + 9^2 + . . . + 30^2\) ?
A. 1,155
B. 1,540
C. 1,925
D. 2,310
E. 3,465
PS19941.02
A. 1,155
B. 1,540
C. 1,925
D. 2,310
E. 3,465
PS19941.02
Key property: \((xy)^n = (x^n)(y^n)\)
So, for example, \(3^2 = (3 \times 1)^2 = (3^2)(1^2)\)
And \(6^2 = (3 \times 2)^2 = (3^2)(2^2)\)
And \(9^2 = (3 \times 3)^2 = (3^2)(3^2)\)
.
.
.
And \(30^2 = (3 \times 10)^2 = (3^2)(10^2)\)
So, \(3^2 + 6^2 + 9^2 + . . . + 30^2 = (3^2)(1^2) + (3^2)(2^2) + (3^2)(3^2) + .... + (3^2)(10^2)\)
\(= 3^2(1^2 + 2^2 + 3^2 + .... + 10^2)\)
\(= 3^2(385)\)
\(= 9(385)\)
\(= 3465\)
Answer: E
RELATED VIDEO
Originally posted by BrentGMATPrepNow on 27 Apr 2020, 15:45.
Last edited by Bunuel on 04 Oct 2023, 02:47, edited 2 times in total.
Last edited by Bunuel on 04 Oct 2023, 02:47, edited 2 times in total.
Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of
[#permalink]
27 Apr 2020, 15:38
27 Apr 2020, 15:38
10
Kudos
\(3^2 + 6^2 + 9^2 + . . . + 30^2\)
= \(3^2(1^2 + 2^2 + 3^2 + . . . + 10^2)\)
= 9*385 = 3465
= \(3^2(1^2 + 2^2 + 3^2 + . . . + 10^2)\)
= 9*385 = 3465
parkhydel wrote:
Given that \(1^2 + 2^2 + 3^2 + . . . + 10^2 = 385\), what is the value of \(3^2 + 6^2 + 9^2 + . . . + 30^2\) ?
A. 1,155
B. 1,540
C. 1,925
D. 2,310
E. 3,465
PS19941.02
A. 1,155
B. 1,540
C. 1,925
D. 2,310
E. 3,465
PS19941.02
