Last visit was: 13 Jul 2024, 08:20 It is currently 13 Jul 2024, 08:20
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Kudos
Tags:
Show Tags
Hide Tags
Manager
Manager
Joined: 03 Jun 2019
Posts: 112
Own Kudos [?]: 10373 [223]
Given Kudos: 39
Most Helpful Reply
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6805
Own Kudos [?]: 30790 [66]
Given Kudos: 799
Location: Canada
Send PM
Retired Moderator
Joined: 19 Oct 2018
Posts: 1868
Own Kudos [?]: 6630 [10]
Given Kudos: 705
Location: India
Send PM
General Discussion
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6020
Own Kudos [?]: 13769 [2]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink]
1
Kudos
1
Bookmarks
Expert Reply
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. \((3*1)^2 + (3*2)^2 + (3*3)^2 + . . . + (3*10)^2 = 3^2*(1^2 + 2^2 + 3^2 + . . . + 10^2) = 3^2*385 = 3465\)

Answer: Option E
Intern
Intern
Joined: 20 Jan 2018
Posts: 24
Own Kudos [?]: 41 [2]
Given Kudos: 57
Location: India
Send PM
Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink]
2
Kudos
Simplify it as
3^2+6^2+... = 3^2(1^2+2^2+..)
Now Solve: 3^2(385)= 3465
Manager
Manager
Joined: 01 Nov 2020
Posts: 85
Own Kudos [?]: 81 [1]
Given Kudos: 52
Send PM
Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink]
1
Kudos
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!
Senior Manager
Senior Manager
Joined: 14 Jul 2019
Status:Student
Posts: 475
Own Kudos [?]: 372 [0]
Given Kudos: 52
Location: United States
Concentration: Accounting, Finance
GMAT 1: 650 Q45 V35
GPA: 3.9
WE:Education (Accounting)
Send PM
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
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6020
Own Kudos [?]: 13769 [0]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink]
Expert Reply
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. :)
CEO
CEO
Joined: 07 Mar 2019
Posts: 2615
Own Kudos [?]: 1864 [0]
Given Kudos: 763
Location: India
WE:Sales (Energy and Utilities)
Send PM
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.

Answer E.
Intern
Intern
Joined: 28 Dec 2020
Posts: 11
Own Kudos [?]: 0 [0]
Given Kudos: 3
Send PM
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
nick1816
Manager
Manager
Joined: 22 Jun 2020
Posts: 154
Own Kudos [?]: 75 [0]
Given Kudos: 120
Location: Georgia
Concentration: Finance, General Management
GMAT 1: 720 Q51 V38
GPA: 3.71
Send PM
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
Director
Director
Joined: 29 Apr 2019
Status:Learning
Posts: 729
Own Kudos [?]: 588 [0]
Given Kudos: 49
Send PM
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 = \(3465\)
Director
Director
Joined: 28 Sep 2018
Posts: 710
Own Kudos [?]: 569 [0]
Given Kudos: 248
GMAT 1: 660 Q48 V33 (Online)
GMAT 2: 700 Q49 V37
Send PM
Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink]
Manager
Manager
Joined: 03 Jul 2020
Posts: 88
Own Kudos [?]: 24 [0]
Given Kudos: 120
Send PM
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.
Intern
Intern
Joined: 17 Jan 2023
Posts: 15
Own Kudos [?]: 1 [0]
Given Kudos: 0
GMAT 1: 740 Q48 V44
Send PM
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
Intern
Intern
Joined: 01 Sep 2019
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 67
Send PM
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
Intern
Intern
Joined: 16 Aug 2022
Posts: 15
Own Kudos [?]: 9 [0]
Given Kudos: 107
Send PM
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)
Intern
Intern
Joined: 14 Feb 2024
Posts: 16
Own Kudos [?]: 8 [0]
Given Kudos: 8
Send PM
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. \((3*1)^2 + (3*2)^2 + (3*3)^2 + . . . + (3*10)^2 = 3^2*(1^2 + 2^2 + 3^2 + . . . + 10^2) = 3^2*385 = 3465\)

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?
GMAT Club Bot
Re: Given that 1^2 + 2^2 + 3^2 + . . . + 10^2 = 385, what is the value of [#permalink]
Moderator:
Math Expert
94327 posts