Last visit was: 18 Nov 2025, 21:01 It is currently 18 Nov 2025, 21:01
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
User avatar
BillyZ
User avatar
Current Student
Joined: 14 Nov 2016
Last visit: 03 May 2025
Posts: 1,143
Own Kudos:
22,214
 [29]
Given Kudos: 926
Location: Malaysia
Concentration: General Management, Strategy
Schools: Sloan '23 (D) Tuck '23 (D) Darden '23 (D) Ross '23 (D) Kellogg '23 (D) Wharton '23 (D) Booth '23 (D) Fuqua '24 (A) Harvard '24 (D) Stanford '24 (D)
GMAT 1: 750 Q51 V40 (Online)
GPA: 3.53
Products:
My Reviews
Schools: Sloan '23 (D) Tuck '23 (D) Darden '23 (D) Ross '23 (D) Kellogg '23 (D) Wharton '23 (D) Booth '23 (D) Fuqua '24 (A) Harvard '24 (D) Stanford '24 (D)
GMAT 1: 750 Q51 V40 (Online)
Posts: 1,143
Kudos: 22,214
 [29]
What is the value of prime number p ? (1) p+8 is prime. 07 Feb 2017, 18:57
3
Kudos
Add Kudos
26
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:

45% (medium)

Question Stats:

65% (01:51) correct 35% (01:34) wrong based on 398 sessions

History

Date
Time
Result
Not Attempted Yet
What is the value of prime number \(p\)?

(1) \(p+8\) is prime.
(2) \(p−8\) is prime.
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
mikemcgarry
User avatar
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Last visit: 06 Aug 2018
Posts: 4,479
Own Kudos:
30,531
 [17]
Given Kudos: 130
Expert
Expert reply
Posts: 4,479
Kudos: 30,531
 [17]
What is the value of prime number p ? (1) p+8 is prime. 08 Feb 2017, 11:59
10
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
ziyuenlau
What is the value of prime number \(p\)?

(1) \(p+8\) is prime.
(2) \(p−8\) is prime.
Show more
Dear ziyuenlau,

I'm happy to respond. :-)

This is a devilishly clever and difficult problem. Let's jump to the case in which we are considering both statements together.

Here are a few number sense rules.
1) In a set of three consecutive integers, one is always divisible by 3.
2) In a set of three evenly spaced integers, one is always divisible by 3.
(These rules generalize from 3 to n.)

The numbers (p - 8), p, and (p + 8) are three evenly spaced numbers, so it absolutely must be true that one of them is divisible by 3. The only way all three of them can be prime is if the one that is divisible by 3 is 3 itself! Thus:
p - 8 = 3
p = 11
p + 8 = 19
If p takes the value p = 11, this is the only way that all three numbers can be prime simultaneously. Thus, the value of p is unique determined. Combined the statements are sufficient. OA = (C).

Veritas wrote a truly beautiful problem here!

Does all this make sense?
Mike :-)
General Discussion
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,092
Given Kudos: 99,964
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: 105,355
Kudos: 778,092
What is the value of prime number p ? (1) p+8 is prime. 08 Feb 2017, 12:22
Kudos
Add Kudos
Bookmarks
Bookmark this Post
mikemcgarry
ziyuenlau
What is the value of prime number \(p\)?

(1) \(p+8\) is prime.
(2) \(p−8\) is prime.
Dear ziyuenlau,

I'm happy to respond. :-)

This is a devilishly clever and difficult problem. Let's jump to the case in which we are considering both statements together.

Here are a few number sense rules.
1) In a set of three consecutive integers, one is always divisible by 3.
2) In a set of three evenly spaced integers, one is always divisible by 3.
(These rules generalize from 3 to n.)

The numbers (p - 8), p, and (p + 8) are three evenly spaced numbers, so it absolutely must be true that one of them is divisible by 3. The only way all three of them can be prime is if the one that is divisible by 3 is 3 itself! Thus:
p - 8 = 3
p = 11
p + 8 = 19
If p takes the value p = 11, this is the only way that all three numbers can be prime simultaneously. Thus, the value of p is unique determined. Combined the statements are sufficient. OA = (C).

Veritas wrote a truly beautiful problem here!

Does all this make sense?
Mike :-)
Show more

This question might be inspired by the following two questions:
https://gmatclub.com/forum/is-the-two-d ... 03359.html
https://gmatclub.com/forum/is-the-posit ... 76553.html
User avatar
AnthonyRitz
User avatar
Stacy Blackman Consulting Director of Test Prep
Joined: 21 Dec 2014
Last visit: 16 Nov 2025
Posts: 238
Own Kudos:
427
 [1]
Given Kudos: 169
Affiliations: Stacy Blackman Consulting
Location: United States (DC)
GMAT 1: 790 Q51 V51
GRE 1: Q170 V170
GRE 2: Q170 V170
GPA: 3.11
WE:Education (Education)
GMAT 1: 790 Q51 V51
GRE 1: Q170 V170
GRE 2: Q170 V170
Posts: 238
Kudos: 427
 [1]
What is the value of prime number p ? (1) p+8 is prime. 08 Feb 2017, 17:43
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thank for the kind words, Mike! (This is one of mine.)

Bunuel, those weren't the inspiration, at least on a conscious level, but it's great to see the convergent evolution; they are certainly excellent and similar questions.

I'm very surprised this is currently listed as sub-600 level. I debated how difficult to go with this one; I could have done something like p - 8, p, p + 20 and gotten the same answer since p + 20 = p + 8 + 12 will be the same remainder w.r.t. 3 as p + 8.
User avatar
AR15J
User avatar
Joined: 21 Aug 2016
Last visit: 15 May 2024
Posts: 214
Own Kudos:
161
 [1]
Given Kudos: 145
Location: India
GPA: 3.9
WE:Information Technology (Computer Software)
Products:
My Reviews
Posts: 214
Kudos: 161
 [1]
What is the value of prime number p ? (1) p+8 is prime. 09 Feb 2017, 10:07
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
mikemcgarry
ziyuenlau
What is the value of prime number \(p\)?

(1) \(p+8\) is prime.
(2) \(p−8\) is prime.
Dear ziyuenlau,

I'm happy to respond. :-)

This is a devilishly clever and difficult problem. Let's jump to the case in which we are considering both statements together.

Here are a few number sense rules.
1) In a set of three consecutive integers, one is always divisible by 3.
2) In a set of three evenly spaced integers, one is always divisible by 3.
(These rules generalize from 3 to n.)

The numbers (p - 8), p, and (p + 8) are three evenly spaced numbers, so it absolutely must be true that one of them is divisible by 3. The only way all three of them can be prime is if the one that is divisible by 3 is 3 itself! Thus:
p - 8 = 3
p = 11
p + 8 = 19
If p takes the value p = 11, this is the only way that all three numbers can be prime simultaneously. Thus, the value of p is unique determined. Combined the statements are sufficient. OA = (C).

Veritas wrote a truly beautiful problem here!

Does all this make sense?
Mike :-)
Show more


Hi mikemcgarry,

I did not understand the rule well.

When you say-- the numbers (p - 8), p, and (p + 8) are three evenly spaced numbers, so it absolutely must be true that one of them is divisible by 3


even spaced means they are at the equal distance from preceding and succeeding term, or distance should be even as well?

For instance--
31 34 37

3 3

but none of them is divisible by 3; I think I misunderstood the concept. Please also explain how this rule is generalized from 3 to n. sorry for the silly question.
User avatar
AnthonyRitz
User avatar
Stacy Blackman Consulting Director of Test Prep
Joined: 21 Dec 2014
Last visit: 16 Nov 2025
Posts: 238
Own Kudos:
427
 [4]
Given Kudos: 169
Affiliations: Stacy Blackman Consulting
Location: United States (DC)
GMAT 1: 790 Q51 V51
GRE 1: Q170 V170
GRE 2: Q170 V170
GPA: 3.11
WE:Education (Education)
GMAT 1: 790 Q51 V51
GRE 1: Q170 V170
GRE 2: Q170 V170
Posts: 238
Kudos: 427
 [4]
What is the value of prime number p ? (1) p+8 is prime. 09 Feb 2017, 10:15
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Good catch, AR15J! To clarify, the rule in question only applies to an evenly spaced set where the spacing isn't itself a multiple of 3.

More broadly, the general rule is this: Any list of N evenly spaced integers will contain a multiple of N as long as the spacing has no factors besides 1 in common with N. (In fact, it will contain exactly one such multiple.)

Try it!
User avatar
AR15J
User avatar
Joined: 21 Aug 2016
Last visit: 15 May 2024
Posts: 214
Own Kudos:
161
Given Kudos: 145
Location: India
GPA: 3.9
WE:Information Technology (Computer Software)
Products:
My Reviews
Posts: 214
Kudos: 161
What is the value of prime number p ? (1) p+8 is prime. 09 Feb 2017, 12:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AnthonyRitz
Good catch, AR15J! To clarify, the rule in question only applies to an evenly spaced set where the spacing isn't itself a multiple of 3.

More broadly, the general rule is this: Any list of N evenly spaced integers will contain a multiple of N as long as the spacing has no factors besides 1 in common with N. (In fact, it will contain exactly one such multiple.)

Try it!
Show more

Thanks AnthonyRitz for clearing the doubt

In GMAT also, evenly spaced means equal distance, below set is also evenly spaced?Please confirm

31,34,37
User avatar
AnthonyRitz
User avatar
Stacy Blackman Consulting Director of Test Prep
Joined: 21 Dec 2014
Last visit: 16 Nov 2025
Posts: 238
Own Kudos:
427
 [1]
Given Kudos: 169
Affiliations: Stacy Blackman Consulting
Location: United States (DC)
GMAT 1: 790 Q51 V51
GRE 1: Q170 V170
GRE 2: Q170 V170
GPA: 3.11
WE:Education (Education)
GMAT 1: 790 Q51 V51
GRE 1: Q170 V170
GRE 2: Q170 V170
Posts: 238
Kudos: 427
 [1]
What is the value of prime number p ? (1) p+8 is prime. 09 Feb 2017, 14:05
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AR15J
AnthonyRitz
Good catch, AR15J! To clarify, the rule in question only applies to an evenly spaced set where the spacing isn't itself a multiple of 3.

More broadly, the general rule is this: Any list of N evenly spaced integers will contain a multiple of N as long as the spacing has no factors besides 1 in common with N. (In fact, it will contain exactly one such multiple.)

Try it!

Thanks AnthonyRitz for clearing the doubt

In GMAT also, evenly spaced means equal distance, below set is also evenly spaced?Please confirm

31,34,37
Show more

AR15J,

Yes, that is correct. 31, 34, 37 is evenly spaced. (But it will never contain a multiple of 3 no matter how long you continue, since the spacing is 3 and since at least one element is not a multiple of 3.) (But if, for instance, you include at least one more element in either direction, you will be guaranteed a multiple of 4.)
User avatar
exc4libur
User avatar
Joined: 24 Nov 2016
Last visit: 22 Mar 2022
Posts: 1,686
Own Kudos:
1,447
Given Kudos: 607
Location: United States
Posts: 1,686
Kudos: 1,447
What is the value of prime number p ? (1) p+8 is prime. 15 Jun 2019, 07:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AnthonyRitz
Any list of N evenly spaced integers will contain a multiple of N as long as the spacing has no factors besides 1 in common with N. (In fact, it will contain exactly one such multiple.)
Show more

Hello Bunuel could you verify this information, because the example below challenges what you AnthonyRitz just said.

For N: 4, Set: {2,4,6,8}, Spacing/Difference: 2; We have a spacing (2) that is a factor of 4 and there is at least one multiple of 4 in the set.

I think the rule is that for any set/list of N evenly spaced integers there is at least one multiple of N:
(1) if any term is a multiple of N; or,
(2) if the common difference (spacing) doesn't share any factors with N but 1.
User avatar
IanStewart
User avatar
GMAT Tutor
Joined: 24 Jun 2008
Last visit: 18 Nov 2025
Posts: 4,145
Own Kudos:
10,985
 [1]
Given Kudos: 99
Expert
Expert reply
Posts: 4,145
Kudos: 10,985
 [1]
What is the value of prime number p ? (1) p+8 is prime. 15 Jun 2019, 07:31
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
exc4libur
AnthonyRitz
Any list of N evenly spaced integers will contain a multiple of N as long as the spacing has no factors besides 1 in common with N. (In fact, it will contain exactly one such multiple.)
AnthonyRitz

Hello, could you verify the information below, because the example below challenges what you just said.

For N: 4, Set: {2,4,6,8}, Spacing/Difference: 2; We have a spacing (2) that is a factor of 4 and there is at least one multiple of 4 in the set.
Show more


What Anthony wrote is correct (though you wouldn't need to know it for the GMAT) - if you create an equally spaced list of N numbers that are d apart, then if the GCD of d and N is 1, the list will contain one multiple of N.

The GCD of N and d in your list is not 1, so it's not a counterexample to that. I think you're trying to establish whether the logical converse of what Anthony wrote is also true, but in math, if you have a true statement, sometimes the converse is also true, and sometimes it's not true in general. And here, the converse is not true in general: when the GCD of N and d is not 1, then we need some more info to say how many multiples of N we'll have in our list. We can't take the converse (reverse) of the true fact above to conclude we should have zero multiples of N - that's only sometimes true.

None of these facts are worth memorizing for the GMAT, though.
User avatar
exc4libur
User avatar
Joined: 24 Nov 2016
Last visit: 22 Mar 2022
Posts: 1,686
Own Kudos:
1,447
Given Kudos: 607
Location: United States
Posts: 1,686
Kudos: 1,447
What is the value of prime number p ? (1) p+8 is prime. 15 Jun 2019, 08:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
IanStewart

What Anthony wrote is correct (though you wouldn't need to know it for the GMAT) - if you create an equally spaced list of N numbers that are d apart, then if the GCD of d and N is 1, the list will contain one multiple of N.

The GCD of N and d in your list is not 1, so it's not a counterexample to that. I think you're trying to establish whether the logical converse of what Anthony wrote is also true, but in math, if you have a true statement, sometimes the converse is also true, and sometimes it's not true in general. And here, the converse is not true in general: when the GCD of N and d is not 1, then we need some more info to say how many multiples of N we'll have in our list. We can't take the converse (reverse) of the true fact above to conclude we should have zero multiples of N - that's only sometimes true.

None of these facts are worth memorizing for the GMAT, though.
Show more

Hi Ian,

Indeed, I was trying to establish the converse. Now I understand.

Thks :)
avatar
Msfollie
avatar
Joined: 17 Aug 2019
Last visit: 29 Jun 2022
Posts: 2
GMAT 1: 650 Q40 V38
GMAT 1: 650 Q40 V38
Posts: 2
Kudos: 0
What is the value of prime number p ? (1) p+8 is prime. 25 Aug 2019, 12:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello, this is my first time posting a question here. I really need to understand why 5 is not a solution here, because in that case, it will satisfy the conditions of (p-8) = -3, and (p+8) = 13, or is it that negative numbers are not considered as prime numbers?
User avatar
siddharth19
User avatar
Joined: 24 Jun 2017
Last visit: 10 Nov 2021
Posts: 27
Own Kudos:
4
Given Kudos: 354
Posts: 27
Kudos: 4
What is the value of prime number p ? (1) p+8 is prime. 26 Aug 2019, 23:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Msfollie
Hello, this is my first time posting a question here. I really need to understand why 5 is not a solution here, because in that case, it will satisfy the conditions of (p-8) = -3, and (p+8) = 13, or is it that negative numbers are not considered as prime numbers?
Show more

hi , prime no.'s are only "positive"by definition . so -3 is not a prime no .
hope it helps :-)
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,587
Own Kudos:
1,079
Posts: 38,587
Kudos: 1,079
What is the value of prime number p ? (1) p+8 is prime. 24 Sep 2024, 00:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
105355 posts
kingbucky
496 posts