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Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of

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parkhydel
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Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink] Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of   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
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E
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BrentGMATPrepNow
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Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink] Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of   Updated on: 04 Oct 2023, 02:47
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parkhydel
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

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.
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nick1816
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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink] Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of   27 Apr 2020, 15:38
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\(3^2 + 6^2 + 9^2 + . . . + 30^2\)

= \(3^2(1^2 + 2^2 + 3^2 + . . . + 10^2)\)

= 9*385 = 3465


parkhydel
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
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GMATinsight
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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink] Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of   27 Apr 2020, 21:18
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parkhydel
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

\(3^2 + 6^2 + 9^2 + . . . + 30^2 = (3*1)^2 + (3*2)^2 + (3*3)^2 + . . . + (3*10)^2\)

CONCEPT: \((a*b)^x = a^x*b^x\)

i.e. \((3*1)^2 + (3*2)^2 + (3*3)^2 + . . . + (3*10)^2 = 3^2*(1^2 + 2^2 + 3^2 + . . . + 10^2) = 3^2*385 = 3465\)

Answer: Option E
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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink] Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of   27 Apr 2020, 21:35
parkhydel
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

3(1^2 + 2^2 +3^2 +....10^2) = 3 *385 = 1,155
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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink] Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of   28 Apr 2020, 01:19
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minustark
parkhydel
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

3(1^2 + 2^2 +3^2 +....10^2) = 3 *385 = 1,155
minustark

A small error. In last step what you take common is 3^2 instead of 3 so your answer is one third of correct answer. :)
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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink] Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of   10 Sep 2020, 09:48
parkhydel
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
\(3^2 + 6^2 + 9^2 + . . . + 30^2\) = \(9 * (1^2 + 2^2 + 3^2 + . . . + 10^2 = 385)\)
Any odd multiple of 5 leaves 5 at unit's place, so B and D are eliminated.

By the time we multiply 9 with 385 and reach tens place i.e. 6 we can pick E as our answer.

Answer E.
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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink] Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of   02 Jan 2021, 07:22
can we solve this by formula:
n/2(a1 + an)=

10/2(9 + 900)=4545
why this approach is incorrect?unraveled
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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink] Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of   13 Mar 2021, 12:12
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YellowBird
can we solve this by formula:
n/2(a1 + an)=

10/2(9 + 900)=4545
why this approach is incorrect?unraveled
GMATinsight
nick1816


We can use the formula only when the sequence is in Arithmetic progression(AP) i.e when the difference between the succeeding number and the preceding number is consistent throughout.

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Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink] Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of   14 Mar 2021, 14:16
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either you have to have magic sight and see that you can rearrange the equality, or you have to be trained almost on every type of GMAT question. God save us all GMAT applicants.

I just wenr ahead with counting like: 30^2=900, 27^2=7**, 24^2=5**, then 441 andso already 900+700+600+441>2600, more than any answer choice, other than E. desperate move, but hope it helps.

Posted from my mobile device
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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink] Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of   08 Sep 2021, 06:07
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Correct option E

as simple as \(3^2\) * 385 = \(3465\)
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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink] Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of   13 Feb 2022, 23:06
Similar Question: https://gmatclub.com/forum/2-239398.html
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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink] Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of   15 Feb 2022, 10:13
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Simplify it as
3^2+6^2+... = 3^2(1^2+2^2+..)
Now Solve: 3^2(385)= 3465
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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink] Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of   03 Nov 2022, 06:33
Took a little longer route. But still made it within 2:33 minutes. Looked at the answer choices. They are far apart.

30 squared is 900.
27 squared is 729.
21 squared is 441
24 squared is more than 441.

900 plus 700 plus 800 = 2600++

Not even counting the others, but after looking at the answer choices only E fits.
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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink] Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of   31 Mar 2023, 10:15
32+62+92+...+302
3
2
+
6
2
+
9
2
+
.
.
.
+
30
2


= 32(12+22+32+...+102)
3
2
(
1
2
+
2
2
+
3
2
+
.
.
.
+
10
2
)


= 9*385 = 3465
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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink] Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of   17 Feb 2024, 09:22
Since, each of the numbers in the set are multiplied by the same number (i.e 3^2), then the sum would also be multiplied by the same number.

Is this conceptually right?

385 * 3^2 = 3465
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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink] Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of   20 Jun 2024, 22:49
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Answer should be multiple of nine (9)
. (E) in the only option = 9 (1+4 +9…xxxx)
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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink] Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of   23 Jun 2024, 13:33
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parkhydel
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
\(3^2 + 6^2 + 9^2 + . . . + 30^2 = (3*1)^2 + (3*2)^2 + (3*3)^2 + . . . + (3*10)^2\)

CONCEPT: \((a*b)^x = a^x*b^x\)

i.e. \((3*1)^2 + (3*2)^2 + (3*3)^2 + . . . + (3*10)^2 = 3^2*(1^2 + 2^2 + 3^2 + . . . + 10^2) = 3^2*385 = 3465\)

Answer: Option E
­I am not sure I understand the theory around how the math/answer was calculated. Would it be possible to further expand?
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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink] Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of   13 Sep 2024, 11:17
\(1^2 + 2^2 + 3^2 + . . . + 10^2 = 385\) (given)

\(3^2+6^2+9^2+......+30^2\) can also be written as

\(3^2+(3*2)^2+(3*3)^2+.......+(3*10)^2\)

this can further simply be written as

\(3^2+3^2*2^2+3^2*3^2+........+3^2*10^2\)

take out \(3^2\) common from the entire sum

\(3^2(1^2+2^2+3^2+.......+10^2)\)

remember that \(1^2 + 2^2 + 3^2 + . . . + 10^2 = 385\) (given)

Hence, we have

\(3^2*385\)
9*385
3465 [ANSWER]
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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink]
13 Sep 2024, 11:17
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