Last visit was: 19 Nov 2025, 21:07 It is currently 19 Nov 2025, 21:07
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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
   1   2   3   4 
655-705 Level|   Math Related|         
User avatar
Lizaza
User avatar
Joined: 16 Jan 2021
Last visit: 17 Nov 2025
Posts: 165
Own Kudos:
219
 [2]
Given Kudos: 5
GMAT 1: 710 Q47 V40
GMAT 1: 710 Q47 V40
Posts: 165
Kudos: 219
 [2]
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 16 Dec 2024, 23:33
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Here, the important thing is that we establish how the numbers will be changing.
Let's visualise this, starting with 1:
  • 1 [not divisible] => \(1+3=4\)
  • 4 [divisible] => \(4+2=6\)
  • 6 [not divisible] => \(6+3=9\)
  • 9 [not divisible] => \(9+3=12\)
  • 12 [divisible] => \(12+2=14 \), etc.

Therefore, if the starting number \(s_4 \) is divisible, then \(s_6\) will be equal to \(s_4 + 5\)
And if it's not divisible, then there're two options possible: \(s_6=s_4+6 \) and \(s_4 + 5\) (as we see from the above variants, where \(6=1+5\), but \(12=6+6\)).

So, checking the answers suggested:
  • \(s_4=5\) (indivisible), so \(s_6=s_4+5=10 \) (not suitable) and \(s_6=s_4+6=11 \) (also not suitable)
  • \(s_4=8\) (divisible), so \(s_6=s_4+5=13 \) (actually suitable)

Hence, the answers are: \(s_4=8, s_6=13\)
User avatar
AbhiS101
User avatar
Joined: 03 Jul 2024
Last visit: 28 Oct 2025
Posts: 80
Own Kudos:
85
 [1]
Given Kudos: 19
Location: India
Schools: IIMA '26 IIMB '26 IIM Calcutta '26 NUS '27
GPA: 68%
Schools: IIMA '26 IIMB '26 IIM Calcutta '26 NUS '27
Posts: 80
Kudos: 85
 [1]
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 17 Dec 2024, 00:09
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 



A sequence of integers is defined using the following logic: If \(s_n\) is divisible by 4, then \(s_{n+1} = s_n + 2\). If \(s_n\) is not divisible by 4, then \(s_{n+1} = s_n + 3\).

Select values for \(s_4\) and \(s_6 \)that are jointly consistent with these conditions. Make only two selections, one in each column.
Show more
Let's assume from that number is divisible by 4
Available options are 8, 12 & 16
for 8 S5th term will be 10 & S6th will be 13

both of these terms satisfy the eqns & available in option

IMO 8 & 13
User avatar
SafSin28
User avatar
Joined: 16 Aug 2022
Last visit: 19 Nov 2025
Posts: 73
Own Kudos:
58
Given Kudos: 56
Posts: 73
Kudos: 58
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers Updated on: 17 Dec 2024, 22:24
Originally posted by SafSin28 on 17 Dec 2024, 00:28.
Last edited by SafSin28 on 17 Dec 2024, 22:24, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Good question
User avatar
tgsankar10
User avatar
Joined: 27 Mar 2024
Last visit: 19 Nov 2025
Posts: 281
Own Kudos:
390
 [1]
Given Kudos: 83
Location: India
Posts: 281
Kudos: 390
 [1]
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 17 Dec 2024, 00:38
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
when \(s_4=8\), \(s_4\) is divisible by \(4\), hence \(s_5=s_4+2=10\)

\(s_5=10\) and it is not divisible by \(4\), hence \(s_6=s_5+3=13\)

Answer:

\(s_4=8\)

\(s_6=13\)
User avatar
NilayMaheshwari
User avatar
Joined: 20 Dec 2023
Last visit: 12 Oct 2025
Posts: 42
Own Kudos:
44
 [1]
Given Kudos: 26
Location: India
GMAT Focus 1: 595 Q80 V82 DI76
Products:
My Reviews
GMAT Focus 1: 595 Q80 V82 DI76
Posts: 42
Kudos: 44
 [1]
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 17 Dec 2024, 00:56
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let's solve from the options.
If s4=5, s5=8, s6=10,
If s4=8, s5=10, s6=13,
If s4=12, s5=14, s6=17,
If s4=13, s5=16, s6=18,
Is s4=16, s5=18, s6=21,
If s4=22, s5=25, s6=28.

Clearly only one case is jointly consistent with the given options, Therefore s4=8, s6=13.

Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 



A sequence of integers is defined using the following logic: If \(s_n\) is divisible by 4, then \(s_{n+1} = s_n + 2\). If \(s_n\) is not divisible by 4, then \(s_{n+1} = s_n + 3\).

Select values for \(s_4\) and \(s_6 \)that are jointly consistent with these conditions. Make only two selections, one in each column.
Show more
User avatar
Invincible_147
User avatar
Joined: 29 Sep 2023
Last visit: 12 Nov 2025
Posts: 73
Own Kudos:
64
 [1]
Given Kudos: 164
Products:
GMAT Club Tests
Posts: 73
Kudos: 64
 [1]
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 17 Dec 2024, 01:16
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi All,

According to me,

If we try by hit and trail with the options for s4 , the sequence fits correct when s4=8 , as 8 is divisible by 4 so s5=8+2-->10 and 10 is not divisible by 4 so s6=10+3 --> 13

therefore s4=8 and s6=13
User avatar
Purnank
User avatar
Joined: 05 Jan 2024
Last visit: 15 Nov 2025
Posts: 680
Own Kudos:
585
 [1]
Given Kudos: 166
Location: India
Concentration: General Management, Strategy
GMAT Focus 1: 635 Q88 V76 DI80
Products:
My Reviews
GMAT Focus 1: 635 Q88 V76 DI80
Posts: 680
Kudos: 585
 [1]
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 17 Dec 2024, 01:40
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 



A sequence of integers is defined using the following logic: If \(s_n\) is divisible by 4, then \(s_{n+1} = s_n + 2\). If \(s_n\) is not divisible by 4, then \(s_{n+1} = s_n + 3\).

Select values for \(s_4\) and \(s_6 \)that are jointly consistent with these conditions. Make only two selections, one in each column.
Show more
Trial and Error method will work here

lets first check value of S4 by considering each values
1st - S4 = 5 (not divisible by 4) Therefore S5 = S4 + 3 = 5+3 = 8 (divisible by 4) Therefore S6 = S5 + 2 = 8+2 = 10 (Not there in table So S4=5 not possible solution)
Similarly,
2nd - S4 = 8 (divisible by 4), We will get S5 = S4+2 = 10 (not divisible by 4) S6 = S5+3 = 10+3 = 13 (There in the table) lets keep this solution and check the rest.
3rd - S4 = 12, S5 = S4 + 2 = 14 Now S6 = S5 + 3 = 17 (Not there in table)
4th - S4 = 13, S5 = S4 + 3 = 16 Now S6 = S5 + 2 = 18 (Not there in table)
5th - S4 = 16, S5 = S4 + 2 = 18 Now S6 = S5 + 3 = 21 (Not there in table)
Plus there is no point in checking S4 = 22 as S6 will be higher so the second condition satisfies.
Therefore, S4 = 8 and S6 = 13.
User avatar
varunkeeja
User avatar
Joined: 30 Oct 2020
Last visit: 14 Nov 2025
Posts: 13
Own Kudos:
12
Given Kudos: 67
Posts: 13
Kudos: 12
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 17 Dec 2024, 02:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
start with s3 as 1 and work till s4 and s6 matches the options given.
avatar
Nipunh
avatar
Joined: 15 Jun 2024
Last visit: 18 Nov 2025
Posts: 168
Own Kudos:
128
Given Kudos: 444
Location: India
Concentration: Strategy, Finance
Schools: HBS '26 ISB '26 IIMB
GMAT Focus 1: 635 Q85 V84 DI75
GPA: 3.556
WE:Research (Consulting)
Schools: HBS '26 ISB '26 IIMB
GMAT Focus 1: 635 Q85 V84 DI75
Posts: 168
Kudos: 128
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 17 Dec 2024, 03:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
let's do this one the lazy way: let the terms s6and s4 both be not div by 4... we then get a difference of 6, only 1 possible solution: 16,22.
User avatar
seenuvasan
User avatar
Joined: 15 Oct 2016
Last visit: 14 Jan 2025
Posts: 18
Own Kudos:
20
 [1]
GMAT 1: 680 Q50 V30
GMAT 1: 680 Q50 V30
Posts: 18
Kudos: 20
 [1]
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 17 Dec 2024, 04:02
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
It is easy to go from choices given. Let's consider S4 is 5, it is not divisible by 4 that gives S5 is 8. S5 is divisible by 4, so it gives S6 is 10. But there is no choice for 10.

Same way by checking S4 is 8 ---> S5 is 10 ---> S6 is 13. We have both the numbers in the columns.

So the answers are s4 = 8 and s6 = 13

(OR)

Alternative way is there is only one term between S4 and S6. So, the possible difference between s4 and s6 is 5 (when one of s4 or s5 value is divisible by 4) or 6 (when s4 and s5 are not divisible by 4).

So let's check with difference is 5. Only 8 and 13 pair gives the difference is 5. So those are the correct answers.
User avatar
webarebears
User avatar
Joined: 22 Jul 2024
Last visit: 15 Apr 2025
Posts: 20
Own Kudos:
17
 [1]
Given Kudos: 80
Location: Indonesia
Schools: MIT '27 (D)
GMAT Focus 1: 625 Q80 V81 DI82
GPA: 3.81
Schools: MIT '27 (D)
GMAT Focus 1: 625 Q80 V81 DI82
Posts: 20
Kudos: 17
 [1]
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 17 Dec 2024, 04:38
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Quote:
A sequence of integers is defined using the following logic: If \(s_n\) is divisible by 4, then \(s_{n+1} = s_n + 2\). If \(s_n\) is not divisible by 4, then \(s_{n+1} = s_n + 3\).

Select values for \(s_4\) and \(s_6 \)that are jointly consistent with these conditions. Make only two selections, one in each column.
Show more

It's better to test the answer, starting from the lower number \(s_4\)
If \(s_4\) = 8, it is divisible by 4
then \(s_5\) = \(s_4\)+2 = 8+2 = 10

Since \(s_5\)=10 and is not divisible by 4,
then \(s_6\)= \(s_5\)+3 = 10+3 = 13
User avatar
skry209
User avatar
Joined: 16 Nov 2024
Last visit: 04 Feb 2025
Posts: 27
Own Kudos:
36
Given Kudos: 1
Posts: 27
Kudos: 36
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 17 Dec 2024, 06:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
without loss of generality, suppose S0 is divisible by 4.
S1= S0+2
S2 = S1+3 = S0 + 5, since S1 is not divisible by 4
S3 = S2+3 = S0 + 8, since S2 is not divisible by 4
S4 = S3+2 = S0 + 10, since S3 = S0 + 8, which is divisible by 4
S5 = S4+3 = S0 + 13, since S4 = S0 + 10, which is not divisible by 4
S6 = S5+3 = S0 + 16, since S5 = S0 + 13, which is not divisible by 4

S6 - S4 = S0 + 16 - S0 + 10 = 6
Only two values from the options match, where the difference between two terms is 6 - 16,22.
User avatar
Prakhar9802
User avatar
Joined: 07 Aug 2023
Last visit: 14 Nov 2025
Posts: 63
Own Kudos:
67
 [1]
Given Kudos: 1
Posts: 63
Kudos: 67
 [1]
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 17 Dec 2024, 07:04
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hit and trial method -

If S4 is 5, then it will follow the second equation for S5 as 5 is not divisible by 4.
So, S5 = S4 + 3 = 5+3 = 8.
Since S5 = 8 is divisible by 4, it will follow equation 1 for S6.
S6 = S5 + 2 = 8 + 2 = 10.

10 is not in the options, hence, not correct.

If S4 is 8, then, for S5, it will follow equation 1 as 8 is divisible by 4.
So, S5 = S4 + 2 = 8+2 = 10.
Since S5 is not divisible by 4, it will follow equation 2 for S6.

S6 = S5 + 3 = 10 + 3 = 13.

S4 = 8, S6 = 13.
Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 



A sequence of integers is defined using the following logic: If \(s_n\) is divisible by 4, then \(s_{n+1} = s_n + 2\). If \(s_n\) is not divisible by 4, then \(s_{n+1} = s_n + 3\).

Select values for \(s_4\) and \(s_6 \)that are jointly consistent with these conditions. Make only two selections, one in each column.
Show more
User avatar
kingbucky
User avatar
Joined: 28 Jul 2023
Last visit: 08 Nov 2025
Posts: 496
Own Kudos:
520
 [1]
Given Kudos: 328
Location: India
Products:
My Reviews
Posts: 496
Kudos: 520
 [1]
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 17 Dec 2024, 07:50
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Lets note that the sequence \(s_n, s_{n+1}\) is always increasing no matter whether s_n is divisbile by 4 or not.
Now, lets plug and chuck values for s_4 in the ascending order of options.
After plugging 5 for s_4 gives 10 for s_6 ;
plugging 8 for s_4 gives 13 for s_6. Hence (8,13) pair is consistent with the criterion set. Hence is the right option !

Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 



A sequence of integers is defined using the following logic: If \(s_n\) is divisible by 4, then \(s_{n+1} = s_n + 2\). If \(s_n\) is not divisible by 4, then \(s_{n+1} = s_n + 3\).

Select values for \(s_4\) and \(s_6 \)that are jointly consistent with these conditions. Make only two selections, one in each column.
Show more
User avatar
HarshaBujji
User avatar
Joined: 29 Jun 2020
Last visit: 16 Nov 2025
Posts: 695
Own Kudos:
885
 [1]
Given Kudos: 247
Location: India
Products:
My Reviews
Posts: 695
Kudos: 885
 [1]
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 17 Dec 2024, 07:51
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 



A sequence of integers is defined using the following logic: If \(s_n\) is divisible by 4, then \(s_{n+1} = s_n + 2\). If \(s_n\) is not divisible by 4, then \(s_{n+1} = s_n + 3\).

Select values for \(s_4\) and \(s_6 \)that are jointly consistent with these conditions. Make only two selections, one in each column.
Show more
This kind of question we need to go by option. So let's pick s4 first and then see if corresponding s6 is present or not.

s4 =5, s5 = 8, s6 = 10. (Not avb)
s4=8, s5=10, s6 =13. (Avb)

Hence s4 = 8, s6 =13
User avatar
Mardee
User avatar
Joined: 22 Nov 2022
Last visit: 16 Oct 2025
Posts: 127
Own Kudos:
110
 [1]
Given Kudos: 17
Products:
GMAT Club Tests
Posts: 127
Kudos: 110
 [1]
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 17 Dec 2024, 07:52
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
From the above question, we observe a pattern in the numbers in the series

lets say the number x is divisible by 4,the next number is x+2 which isnt divisible by 4, then it gets converted to x+5, which is not divisible by 4, then it gets converted to x+8 which is divisble by 4, and repeat

So the series is x, x+2, x+5, x+8, x+10,....

So from that we can see,
if we substitute s4 as 8 then s6 would be 13
User avatar
Jayesh20201
User avatar
Joined: 18 Sep 2023
Last visit: 17 Nov 2025
Posts: 10
Own Kudos:
7
 [1]
Given Kudos: 45
Posts: 10
Kudos: 7
 [1]
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 17 Dec 2024, 08:48
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 



A sequence of integers is defined using the following logic: If \(s_n\) is divisible by 4, then \(s_{n+1} = s_n + 2\). If \(s_n\) is not divisible by 4, then \(s_{n+1} = s_n + 3\).

Select values for \(s_4\) and \(s_6 \)that are jointly consistent with these conditions. Make only two selections, one in each column.
Show more

The best thing to understand is to ascertain that the values are ascending i.e. increasing from S1 to S2 to S3 and so on.
Which means that between s4 to s6 as well the values increase.

Now, trial and error worked best for me. So,
I. if S4 = 5 then S5=8 (s4 not divisible by 4, so add 3) and S6=10 (s5 divisible by 4, so add 2)
II. if S4 = 8 then S5=10 (s4 divisible by 4, so add 2) and S6=13 (s5 not divisible by 4, so add 3) Jackppot.

If you try this with others, Option B and C for I and II respectively will still stand. Trust yourself and avoid redundancies.
User avatar
ravi1522
User avatar
Joined: 05 Jan 2023
Last visit: 19 Nov 2025
Posts: 116
Own Kudos:
70
 [1]
Given Kudos: 5
Location: India
Concentration: General Management, General Management
Schools: INSEAD Aug '26 HEC Sept '26 LBS '26
GMAT Focus 1: 595 Q80 V83 DI76
GMAT 1: 530 Q38 V24
GPA: 7.2
WE:Design (Real Estate)
Products:
GMAT Club Tests
Schools: INSEAD Aug '26 HEC Sept '26 LBS '26
GMAT Focus 1: 595 Q80 V83 DI76
GMAT 1: 530 Q38 V24
Posts: 116
Kudos: 70
 [1]
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 17 Dec 2024, 08:54
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hii,
Lets take S4=8
as it is divisible by 4 then S5 =10
as S5 is not divisible by 4 so
S6 will be 13
so pair will be S4 =8
S6=13
Thanks
User avatar
Ayeka
User avatar
Joined: 26 May 2024
Last visit: 13 Nov 2025
Posts: 439
Own Kudos:
317
Given Kudos: 158
Location: India
Schools: ISB
GMAT Focus 1: 645 Q82 V83 DI80
GPA: 4.2
Schools: ISB
GMAT Focus 1: 645 Q82 V83 DI80
Posts: 439
Kudos: 317
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 18 Dec 2024, 08:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
S4= 8
8 is divisible by 4, so S5=10
10 is not divisible by 4, so S6=13

(S4,S6) = (8,13)
User avatar
HansikaSachdeva
User avatar
Joined: 17 May 2024
Last visit: 17 Nov 2025
Posts: 60
Own Kudos:
64
Given Kudos: 143
Location: India
Concentration: Social Entrepreneurship, Sustainability
Products:
GMAT Club Tests Forum Quiz
Posts: 60
Kudos: 64
12 Days of Christmas GMAT Competition - Day 1: A sequence of integers 21 Dec 2024, 09:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Analyzing the conditions given,
If \(s_n\) is divisible by 4, the difference between consecutive terms is 2
If \(s_n\) is not divisible by 4, the difference between consecutive terms is 3

Let \(s_4\) be 8 (divisible by 4),
\(s_5 = s_4 + 2 = 8 + 2 = 10\)
\(s_6 = s_5 + 3 = 10 + 3 = 13\)

Now let \(s_4\) be 7 (not divisible by 4),
\(s_5 = s_4 + 3 = 7 + 3 = 10\)
\(s_6 = s_5 + 3 = 10 + 3 = 13\)

Answer:
\(s_4\) = 8
\(s_6\) = 13
   1   2   3   4 
Moderators:
Bunuel
Math Expert
105390 posts
kingbucky
496 posts