Last visit was: 25 Apr 2026, 17:41 It is currently 25 Apr 2026, 17:41
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
Sub 505 (Easy)|   Arithmetic|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Apr 2026
Posts: 109,830
Own Kudos:
811,285
 [4]
Given Kudos: 105,886
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: 109,830
Kudos: 811,285
 [4]
If the second term of a harmonic progression is 5 and the 5th term of 10 Jun 2021, 09:00
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

90% (01:00) correct 10% (01:26) wrong based on 163 sessions

History

Date
Time
Result
Not Attempted Yet
Evaluate: 6^2 + 7^2 + 8^2 + 9^2 + 10^2 + 11^2

(A) 449
(B) 450
(C) 451
(D) 452
(E) 453
ShowHide Answer
Official Answer
C
User avatar
unraveled
User avatar
Joined: 07 Mar 2019
Last visit: 10 Apr 2025
Posts: 2,706
Own Kudos:
2,329
Given Kudos: 763
Location: India
WE:Sales (Energy)
Posts: 2,706
Kudos: 2,329
If the second term of a harmonic progression is 5 and the 5th term of 10 Jun 2021, 09:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Evaluate: 6^2 + 7^2 + 8^2 + 9^2 + 10^2 + 11^2

(A) 449
(B) 450
(C) 451
(D) 452
(E) 453
Show more
\(6^2 + 7^2 + 8^2 + 9^2 + 10^2 + 11^2\)
\( = 6^2 + 6^2 + (6+7)*1 + 6^2 + (6+8)*2 + 6^2 + (6+9)*3 + 6^2 + (6+10)*4 + 6^2 + (6+11)*5\)
\( = 6^2*6 + 13 + 28 + 45 + 64 + 85\)
= 216 + 235
= 451

Answer C.
User avatar
AndreaBer
User avatar
Joined: 06 Apr 2021
Last visit: 11 Aug 2021
Posts: 10
Own Kudos:
29
Given Kudos: 15
Posts: 10
Kudos: 29
If the second term of a harmonic progression is 5 and the 5th term of 10 Jun 2021, 09:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
6^2 + 7^2 + 8^2 + 9^2 + 10^2 + 11^2 = 36+49+64+81+100+121= 451

solution: C
User avatar
ProKiller
User avatar
Joined: 22 Jun 2015
Last visit: 25 Sep 2021
Posts: 84
Own Kudos:
57
 [2]
Given Kudos: 135
Status:Learning!
GMAT 1: 580 Q47 V24
GMAT 2: 680 Q48 V33
Products:
My Reviews
GMAT 2: 680 Q48 V33
Posts: 84
Kudos: 57
 [2]
If the second term of a harmonic progression is 5 and the 5th term of 10 Jun 2021, 09:55
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
Evaluate: 6^2 + 7^2 + 8^2 + 9^2 + 10^2 + 11^2

(A) 449
(B) 450
(C) 451
(D) 452
(E) 453
Show more

Sum(n^2) = [n(n+1)(2n+1)] / 6

Approach: Find sum of squares of first 11 natural numbers, and subtract from sum of squares of first 5 natural numbers.

Sum (11) - Sum (5)
= [11(11+1)(2*11+1)] / 6 - [5(5+1)(2*5+1)] / 6
= [11(2)(23)] - [5(11)]
= [11*46] - 55
= 506 - 55
= 451

Option C

P.S. Might not be the shortest possible path, but knowing this approach can be beneficial for other questions.
avatar
VermaPulkit
avatar
Joined: 05 May 2021
Last visit: 02 Aug 2021
Posts: 8
Own Kudos:
6
 [2]
Given Kudos: 60
Posts: 8
Kudos: 6
 [2]
If the second term of a harmonic progression is 5 and the 5th term of 10 Jun 2021, 10:49
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The shortest way is to look at the options and observe the units digit are different for all options :

Hence just add the units digit of the expression:

Units digit for 6^2, 7^2, 8^2, 9^2, 10^2 and 11^2 are 6,9,4,1,0,1 if u add them units digit will come out to be 1

Answer should be C : 451, only answer that has 1 at unit’s place.

Posted from my mobile device
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,986
Own Kudos:
1,118
Posts: 38,986
Kudos: 1,118
If the second term of a harmonic progression is 5 and the 5th term of 01 Oct 2025, 01:20
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
109830 posts
Krunaal
Tuck School Moderator
852 posts