Last visit was: 24 Apr 2026, 23:44 It is currently 24 Apr 2026, 23:44
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: 24 Apr 2026
Posts: 109,819
Own Kudos:
811,100
 [34]
Given Kudos: 105,873
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: 109,819
Kudos: 811,100
 [34]
Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 + S2 – S1. What is the 11 Jun 2015, 04:33
5
Kudos
Add Kudos
29
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

83% (02:41) correct 17% (02:32) wrong based on 692 sessions

History

Date
Time
Result
Not Attempted Yet
Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 + S2 – S1. What is the value of K?

(A) 67
(B) 50
(C) 45
(D) 41
(E) 36
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,819
Own Kudos:
811,100
 [12]
Given Kudos: 105,873
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: 109,819
Kudos: 811,100
 [12]
Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 + S2 – S1. What is the 15 Jun 2015, 01:51
4
Kudos
Add Kudos
8
Bookmarks
Bookmark this Post
Bunuel
Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 + S2 – S1. What is the value of K?

(A) 67
(B) 50
(C) 45
(D) 41
(E) 36


Kudos for a correct solution.
Show more

MANHATTAN GMAT OFFICIAL SOLUTION:

The expression for K becomes more manageable if we insert parentheses:
K = (S6 – S5) + (S4 – S3 )+ (S2 – S1)

K involves two expressions of the form \((S_{n + 1} - S_n)\), so a general rule for \((S_{n + 1} - S_n )\) might be helpful. We know that \(S_n = n^2 + 5n + 94\), so

\(S_{n + 1} = (n + 1)^2 + 5(n + 1) + 94\)
\(S_{n + 1} = (n^2 + 2n + 1) + (5n + 5) + 94\)
\(S_{n + 1} = n^2 + 7n + 100\)

In general, \((S_{n + 1} - S_n) = (n^2 + 7n + 100) - (n^2 + 5n + 94) = 2n + 6\).

Applying this rule to the grouped terms in K:
K = (S6 – S5) + (S4 – S3) + (S2 – S1)
= (2 × 5 + 6) + (2 × 3 + 6) + (2 × 1 + 6)
= 16 + 12 + 8
= 36

Alternatively, we could just plug into the Sn term definition, and identify common terms as we work:
K = S6 – S5 + S4 – S3 + S2 – S1= (6^2 + 5(6) + 94) –(5^2 + 5(5) + 94) + (4^2 + 5(4) + 94) – (3^2 + 5(3) + 94) + (2^2 + 5(2) + 94) – (1^2 +5(1) + 94)= (6^2 – 5^2 + 4^2 – 3^2 + 2^2 – 1^2) + 5(6 – 5 + 4 – 3 + 2 – 1)= (36 – 25 + 16 – 9 + 4 – 1) + 5(3)= (21) + (15)= 36

The correct answer is E.
General Discussion
User avatar
BuggerinOn
User avatar
Joined: 08 Sep 2014
Last visit: 29 Nov 2015
Posts: 22
Own Kudos:
64
 [2]
Given Kudos: 53
Schools: Sauder '18 Schulich Jan '18 Rotman '18 Insead Sept '17
GMAT Date: 07-11-2015
GPA: 2.9
WE:Account Management (Computer Software)
Schools: Sauder '18 Schulich Jan '18 Rotman '18 Insead Sept '17
Posts: 22
Kudos: 64
 [2]
Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 + S2 – S1. What is the 11 Jun 2015, 04:51
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I used brute force for this question:
S6: 36+30+94=160
S5: 25+25+94=144
S4: 16+20+94=130
S3: 9+15+94=118
S2: 4+10+94=108
S1: 1+5+94=101

S6-S5+S4-S3+S2-S1= 16+12+7=36
Answer E
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 24 Apr 2026
Posts: 11,229
Own Kudos:
45,011
 [4]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 45,011
 [4]
Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 + S2 – S1. What is the 11 Jun 2015, 05:19
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel
Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 + S2 – S1. What is the value of K?

(A) 67
(B) 50
(C) 45
(D) 41
(E) 36


Kudos for a correct solution.
Show more

two ways , i would solve it..
1) Sn = n^2 + 5n + 94
K=S6 – S5 + S4 – S3 + S2 – S1
=(6^2-5^2+4^2-3^2+2^2-1^2)+5(6-5+4-3+2-1)+0
=(36-25+16-9+4-1)+5(3)+0=36
2) looking at the choices avail..
we know there are three even terms in +ive and three odd terms in -ive...
so 94 gets cancelled out..
if you add square of three even numbers and subtract square of odd no, it will always be odd..
so n^2 will be odd and 5*n will also be odd, so answer should be even....only B and E are left..


Also if we just concentrate on last digits of n^2 and n.. we can easily see it has to be 6.. only 36 is left
User avatar
reto
User avatar
Retired Moderator
Joined: 29 Apr 2015
Last visit: 24 Aug 2018
Posts: 716
Own Kudos:
4,304
 [2]
Given Kudos: 302
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE:Asset Management (Finance: Investment Banking)
Schools: LBS MIF '19
Posts: 716
Kudos: 4,304
 [2]
Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 + S2 – S1. What is the 12 Jul 2015, 04:06
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 + S2 – S1. What is the value of K?

(A) 67
(B) 50
(C) 45
(D) 41
(E) 36


Kudos for a correct solution.
Show more

Can I just ignore the "+94" in the first equation because we always have a subtraction between Sn - S(n-1)? Like this:

S6-S5 = 6^2 + 5*6 - 5^2 +5*5 =16
S4-S3 = 4^2 + 5*4 - 3^2 + 5*3 = 12
S2-S1 = 2^2 + 2*5 - 1 + 5 = 8
User avatar
ENGRTOMBA2018
User avatar
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
Posts: 2,319
Own Kudos:
3,890
 [1]
Given Kudos: 816
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Products:
My Reviews
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
Posts: 2,319
Kudos: 3,890
 [1]
Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 + S2 – S1. What is the 12 Jul 2015, 04:27
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
reto
Bunuel
Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 + S2 – S1. What is the value of K?

(A) 67
(B) 50
(C) 45
(D) 41
(E) 36


Kudos for a correct solution.

Can I just ignore the "+94" in the first equation because we always have a subtraction between Sn - S(n-1)? Like this:

S6-S5 = 6^2 + 5*6 - 5^2 +5*5 =16
S4-S3 = 4^2 + 5*4 - 3^2 + 5*3 = 12
S2-S1 = 2^2 + 2*5 - 1 + 5 = 8
Show more

Yes, you can ignore 94 but only because the number of negative terms = number of positive terms and the coefficients of positive terms (all are 1) = coefficients of negative terms (all are 1).

Had it been : s5-s4+s3-s2+s1 , you could not have 'ignored' 94 as the number of terms for positive vs negative are not equal. So 94 would not have been cancelled.

Also, if it had been: s4- 3s3 + 2s2-s1 , even in this case, you can not ignore 94 (you might still be able to cancel all 94s but you should follow a systematic approach for questions that will provide highest ROI with least scope of error.
User avatar
Nunuboy1994
User avatar
Joined: 12 Nov 2016
Last visit: 24 Apr 2019
Posts: 554
Own Kudos:
126
 [1]
Given Kudos: 167
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
Posts: 554
Kudos: 126
 [1]
Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 + S2 – S1. What is the 19 Feb 2017, 20:55
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel- how were we supposed to know that s6 meant plug in 6 for n and s5 meant plug in 5 for n? I have not seen this is any of my prep materials. Maybe I am dumb- but I was not able to draw that inference from the question.
User avatar
RastogiSarthak99
User avatar
Joined: 20 Mar 2019
Last visit: 10 Aug 2024
Posts: 139
Own Kudos:
26
 [2]
Given Kudos: 282
Location: India
Posts: 139
Kudos: 26
 [2]
Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 + S2 – S1. What is the 07 Aug 2022, 03:20
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
My 2 cents on this:

I don't think this is a tough question. I do however think this question can take time if not done properly.

The way I grouped these statements were as follows:

= 6^2-5^2 + 4^-3^2 + 2^2 - 1^2

+ 30 - 25 + 20-15 + 10 - 5

+ 94-94+94-94+94-94

= 21 + 15
= 36

E.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,978
Own Kudos:
1,117
Posts: 38,978
Kudos: 1,117
Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 + S2 – S1. What is the 21 Jan 2026, 06:30
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
109818 posts
Krunaal
Tuck School Moderator
853 posts