Last visit was: 21 Apr 2026, 15:43 It is currently 21 Apr 2026, 15:43
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 21 Apr 2026
Posts: 109,728
Own Kudos:
810,465
 [29]
Given Kudos: 105,800
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,728
Kudos: 810,465
 [29]
What is the value of (1^2 + 2^2 + ... + 10^2)/(1 + 2 + ...+ 10)? 10 Nov 2023, 04:32
Kudos
Add Kudos
28
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

75% (02:15) correct 25% (02:11) wrong based on 544 sessions

History

Date
Time
Result
Not Attempted Yet
What is the value of \(\frac{1^2+2^2+...+10^2}{1+2+...+10}\)?

(A) 7/3
(B) 7/2
(C) 5
(D) 7
(E) 14
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
VivekSri
User avatar
Joined: 01 May 2022
Last visit: 05 Feb 2026
Posts: 468
Own Kudos:
769
 [15]
Given Kudos: 117
Location: India
WE:Engineering (Consulting)
Posts: 468
Kudos: 769
 [15]
What is the value of (1^2 + 2^2 + ... + 10^2)/(1 + 2 + ...+ 10)? 10 Nov 2023, 04:44
7
Kudos
Add Kudos
8
Bookmarks
Bookmark this Post
Bunuel
What is the value of \(\frac{1^2+2^2+...+10^2}{1+2+...+10}\)?

(A) 7/3
(B) 7/2
(C) 5
(D) 7
(E) 14
Show more

These are the most important formula that we must revise
Sum of squares of first n natural numbers -> [n(n+1)(2n+1)] / 6
Sum of squares of first n even numbers -> [2n(n + 1)(2n + 1)] / 3
Sum of squares of first n odd numbers -> [n(2n+1)(2n-1)] / 3

Sum of first n number = n(n+1)/2

Now to solve this
Numerator is square of first n number where n = 10
and denominator is sum of first n number where n = 10

Numerator = \(\frac{[n(n+1)(2n+1)]*2 }{ 6*n(n+1)}\) = \(\frac{2n+1 }{3}\)= 21/3 = 7
OA is D
General Discussion
avatar
ManifestDreamMBA
avatar
Joined: 17 Sep 2024
Last visit: 21 Feb 2026
Posts: 1,387
Own Kudos:
897
 [1]
Given Kudos: 243
Posts: 1,387
Kudos: 897
 [1]
What is the value of (1^2 + 2^2 + ... + 10^2)/(1 + 2 + ...+ 10)? 07 Dec 2024, 09:38
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Is there an alternate solution to this if one doesn't know the formula?
User avatar
mtt97
User avatar
Joined: 31 May 2024
Last visit: 12 May 2025
Posts: 6
Own Kudos:
4
 [1]
Given Kudos: 10
Location: Peru
Schools: Said '27 (A$) McCombs '27 (A) HEC '26 (A) Haas '27 (WL) INSEAD '26 (A)
Products:
My Reviews
Schools: Said '27 (A$) McCombs '27 (A) HEC '26 (A) Haas '27 (WL) INSEAD '26 (A)
Posts: 6
Kudos: 4
 [1]
What is the value of (1^2 + 2^2 + ... + 10^2)/(1 + 2 + ...+ 10)? 07 Dec 2024, 12:55
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I did it with brut force:

1+4+9+16+25+36+49+64+81+100

Then, I tried to match numbers for easy calculations:

100
81+9= 90
36+64=100
4+16=20
49+1 = 50
25

100+100+90+50+20+25 = 385

Same with the denominator:
1+2+3+4+5+6+7+8+9+10

10
1+9=10
8+2=10
7+3=10
6+4=10
5

10*5+5=55

385/55=7



ManifestDreamMBA
Is there an alternate solution to this if one doesn't know the formula?
Show more
avatar
ManifestDreamMBA
avatar
Joined: 17 Sep 2024
Last visit: 21 Feb 2026
Posts: 1,387
Own Kudos:
897
Given Kudos: 243
Posts: 1,387
Kudos: 897
What is the value of (1^2 + 2^2 + ... + 10^2)/(1 + 2 + ...+ 10)? 08 Dec 2024, 13:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thanks, I followed these annoying calculations too. But was wondering if there's another approach, given a lot of GMAT questions don't need these not so common formula.

Btw, the denominator can be calculated using the mean * number of terms or n(n+1)/2 formula (this one is pretty common, don't want to contradict what i just mentioned above, :D )
Mariana_Taramona
I did it with brut force:

1+4+9+16+25+36+49+64+81+100

Then, I tried to match numbers for easy calculations:

100
81+9= 90
36+64=100
4+16=20
49+1 = 50
25

100+100+90+50+20+25 = 385

Same with the denominator:
1+2+3+4+5+6+7+8+9+10

10
1+9=10
8+2=10
7+3=10
6+4=10
5

10*5+5=55

385/55=7



ManifestDreamMBA
Is there an alternate solution to this if one doesn't know the formula?
Show more
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,956
Own Kudos:
1,117
Posts: 38,956
Kudos: 1,117
What is the value of (1^2 + 2^2 + ... + 10^2)/(1 + 2 + ...+ 10)? 26 Dec 2025, 09:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109728 posts
Krunaal
Tuck School Moderator
853 posts