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

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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink]
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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

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

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

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

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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink]
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

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]
minustark wrote:
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

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]
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

$$3^2 + 6^2 + 9^2 + . . . + 30^2$$ = $$9 * (1^2 + 2^2 + 3^2 + . . . + 10^2 = 385)$$
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.

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

10/2(9 + 900)=4545
why this approach is incorrect?unraveled
GMATinsight
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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink]
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YellowBird wrote:
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.

Kudos, if helped!
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Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink]
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]
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]
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Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink]
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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]
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]
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]
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]
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]
GMATinsight wrote:
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

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

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

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