Last visit was: 23 Apr 2026, 14:18 It is currently 23 Apr 2026, 14:18
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
505-555 (Easy)|   Remainders|      
User avatar
aeros232
User avatar
Joined: 04 Sep 2009
Last visit: 22 Jul 2013
Posts: 31
Own Kudos:
329
 [9]
Given Kudos: 9
Posts: 31
Kudos: 329
 [9]
When integer r is divided by 7, the remainder is 3. When Updated on: 30 Sep 2012, 04:39
Originally posted by aeros232 on 29 Sep 2012, 13:14.
Last edited by Bunuel on 30 Sep 2012, 04:39, edited 2 times in total.
Renamed the topic and edited the question.
1
Kudos
Add Kudos
8
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:

79% (01:29) correct 21% (01:42) wrong based on 308 sessions

History

Date
Time
Result
Not Attempted Yet
When integer r is divided by 7, the remainder is 3. When integer s is divided by 7, the remainder is 3 also. What is the remainder when r^2 - s is divided by 7?

A. 2
B. 3
C. 4
D. 5
E. 6
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
EvaJager
User avatar
Joined: 22 Mar 2011
Last visit: 31 Aug 2016
Posts: 513
Own Kudos:
2,370
 [5]
Given Kudos: 43
WE:Science (Education)
Posts: 513
Kudos: 2,370
 [5]
When integer r is divided by 7, the remainder is 3. When 29 Sep 2012, 14:50
2
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
aeros232
52. When integer r is divided by 7, the remainder is 3. When integer s is divided by 7, the remainder is 3 also. What is the remainder when r^2 < s is divided by 7?

Show Spoiler
e

a. 2
b. 3
c. 4
d. 5
e. 6
Show more

It should be \(r^2-s\) and not \(r^2<s\).

\(r=7a+3\) for some integer \(a\) and \(s=7b+3\) for some integer \(b.\)
Then \(r^2\) is a multiple M7 + 2 (multiple of 7 plus 2), so the difference \(r^2-s\) is M7 + 2 - 3 = M7 - 1 = M7 - 7 + 6 which is M7 + 6.

Answer E.
General Discussion
User avatar
aeros232
User avatar
Joined: 04 Sep 2009
Last visit: 22 Jul 2013
Posts: 31
Own Kudos:
329
Given Kudos: 9
Posts: 31
Kudos: 329
When integer r is divided by 7, the remainder is 3. When 29 Sep 2012, 15:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EvaJager
aeros232
52. When integer r is divided by 7, the remainder is 3. When integer s is divided by 7, the remainder is 3 also. What is the remainder when r^2 < s is divided by 7?

Show Spoiler
e

a. 2
b. 3
c. 4
d. 5
e. 6

It should be \(r^2-s\) and not \(r^2<s\).

\(r=7a+3\) for some integer \(a\) and \(s=7b+3\) for some integer \(b.\)
Then \(r^2\) is a multiple M7 + 2 (multiple of 7 plus 2), so the difference \(r^2-s\) is M7 + 2 - 3 = M7 - 1 = M7 - 7 + 6 which is M7 + 6.

Answer E.
Show more

Yes, you are right!!! And by the way, excellent explanation, thanks!!
User avatar
sanjoo
User avatar
Joined: 06 Aug 2011
Last visit: 24 Dec 2016
Posts: 266
Own Kudos:
680
 [2]
Given Kudos: 82
Posts: 266
Kudos: 680
 [2]
When integer r is divided by 7, the remainder is 3. When 29 Sep 2012, 23:52
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
aeros232
52. When integer r is divided by 7, the remainder is 3. When integer s is divided by 7, the remainder is 3 also. What is the remainder when r^2 - s is divided by 7?

Show Spoiler
e

a. 2
b. 3
c. 4
d. 5
e. 6
Show more

i would suggest to take num rather than doing it algerabically.

take 10.. when it divided by 7 it will have remainder 3..
So R=10..

S will also B 10..

Square of 10..=100

r2-s..100-10=90..

90 /7 ..u l have remained 6 ..

Hope it helps !
avatar
rueyaroo
avatar
Joined: 26 Sep 2012
Last visit: 03 Jun 2013
Posts: 1
Own Kudos:
1
 [1]
Posts: 1
Kudos: 1
 [1]
When integer r is divided by 7, the remainder is 3. When 30 Sep 2012, 00:06
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
aeros232
52. When integer r is divided by 7, the remainder is 3. When integer s is divided by 7, the remainder is 3 also. What is the remainder when r^2 - s is divided by 7?

Show Spoiler
e

a. 2
b. 3
c. 4
d. 5
e. 6
Show more

I was wondering if my approach is okay.. Here's my work.
r/7 = 3
s/7 = 3
r^2 - s / 7
Since everything is divided by 7, you can cancel all of those out.
R = S
R = 3
S = 3

so.. 3^2 - 3 = 6
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,785
Own Kudos:
810,852
 [1]
Given Kudos: 105,853
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: 109,785
Kudos: 810,852
 [1]
When integer r is divided by 7, the remainder is 3. When 01 Oct 2012, 06:47
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sanjoo
aeros232
52. When integer r is divided by 7, the remainder is 3. When integer s is divided by 7, the remainder is 3 also. What is the remainder when r^2 - s is divided by 7?

Show Spoiler
e

a. 2
b. 3
c. 4
d. 5
e. 6

i would suggest to take num rather than doing it algerabically.

take 10.. when it divided by 7 it will have remainder 3..
So R=10..

S will also B 10..

Square of 10..=100

r2-s..100-10=90..

90 /7 ..u l have remained 6 ..

Hope it helps !
Show more

That's correct. +1.

r^2 - s must yield the same reminder when divided by 7 for every r and s which satisfy the given conditions. Thus picking numbers would be the easiest way to deal with this question.
User avatar
sanjoo
User avatar
Joined: 06 Aug 2011
Last visit: 24 Dec 2016
Posts: 266
Own Kudos:
680
Given Kudos: 82
Posts: 266
Kudos: 680
When integer r is divided by 7, the remainder is 3. When 01 Oct 2012, 09:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
sanjoo
aeros232
52. When integer r is divided by 7, the remainder is 3. When integer s is divided by 7, the remainder is 3 also. What is the remainder when r^2 - s is divided by 7?

Show Spoiler
e

a. 2
b. 3
c. 4
d. 5
e. 6

i would suggest to take num rather than doing it algerabically.

take 10.. when it divided by 7 it will have remainder 3..
So R=10..

S will also B 10..

Square of 10..=100

r2-s..100-10=90..

90 /7 ..u l have remained 6 ..

Hope it helps !

That's correct. +1.

r^2 - s must yield the same reminder when divided by 7 for every r and s which satisfy the given conditions. Thus picking numbers would be the easiest way to deal with this question.
Show more


Thanks for kudos ..MATH GURU..:)..
avatar
Ousmane
avatar
Joined: 11 Jul 2012
Last visit: 28 Sep 2018
Posts: 34
Own Kudos:
28
Posts: 34
Kudos: 28
When integer r is divided by 7, the remainder is 3. When 26 Oct 2012, 13:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Or alternatively
r = 7x + 3
s = 7y + 3
r^2 = 49x^2+ 7*3*2 + 9
r^2 - s = 7*7x^2+ 7*3*2 + 9 - 7y + 3 = 7(7x^2+6) +6 = 7Q + 6
Remainder is 6
Brother Karamazov
User avatar
gracie
User avatar
Joined: 07 Dec 2014
Last visit: 11 Oct 2020
Posts: 1,028
Own Kudos:
2,022
Given Kudos: 27
Posts: 1,028
Kudos: 2,022
When integer r is divided by 7, the remainder is 3. When 08 Dec 2017, 13:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

r^2 - s must yield the same reminder when divided by 7 for every r and s which satisfy the given conditions. Thus picking numbers would be the easiest way to deal with this question.
Show more

this doesn't seem to work when r=3 and s=10
not sure why
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,785
Own Kudos:
810,852
Given Kudos: 105,853
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: 109,785
Kudos: 810,852
When integer r is divided by 7, the remainder is 3. When 08 Dec 2017, 22:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gracie
Bunuel

r^2 - s must yield the same reminder when divided by 7 for every r and s which satisfy the given conditions. Thus picking numbers would be the easiest way to deal with this question.

this doesn't seem to work when r=3 and s=10
not sure why
Show more

If r = 3 and s = 10, then r^2 - s = -1. The remainder when -1 id divided by 7 is also 6.
User avatar
laddaboy
User avatar
Joined: 22 May 2015
Last visit: 20 Oct 2024
Posts: 105
Own Kudos:
110
Given Kudos: 26
Posts: 105
Kudos: 110
When integer r is divided by 7, the remainder is 3. When 21 Jun 2019, 20:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Since we have absolute values in answer, plugged in 10,17 so 100 - 17 = 83, reminder 6
User avatar
pdavulur
User avatar
Joined: 22 Jun 2023
Last visit: 19 Oct 2023
Posts: 6
Given Kudos: 35
Posts: 6
Kudos: 0
When integer r is divided by 7, the remainder is 3. When 29 Aug 2023, 04:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sanjoo
aeros232
52. When integer r is divided by 7, the remainder is 3. When integer s is divided by 7, the remainder is 3 also. What is the remainder when r^2 - s is divided by 7?

Show Spoiler
e

a. 2
b. 3
c. 4
d. 5
e. 6

i would suggest to take num rather than doing it algerabically.

take 10.. when it divided by 7 it will have remainder 3..
So R=10..

S will also B 10..

Square of 10..=100

r2-s..100-10=90..

90 /7 ..u l have remained 6 ..

Hope it helps !
Show more

Hi Sanjoo,

In this method, how do we know if R=S?
If R=10, S can be 3 or 10 or 17 etc, isn't it?
If S=3, then r2-s=100-9=91, 91/7 gives a remainder of 0.
If S=10, then as per the calculation, we get a remainder of 6.
Wondering if I missed something here?
User avatar
Nabneet
User avatar
Joined: 27 Dec 2022
Last visit: 19 Aug 2024
Posts: 105
Own Kudos:
120
 [1]
Given Kudos: 40
Location: India
GMAT 1: 550 Q47 V20
WE:Other (Other)
GMAT 1: 550 Q47 V20
Posts: 105
Kudos: 120
 [1]
When integer r is divided by 7, the remainder is 3. When 29 Aug 2023, 07:29
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
pdavulur
sanjoo
aeros232
52. When integer r is divided by 7, the remainder is 3. When integer s is divided by 7, the remainder is 3 also. What is the remainder when r^2 - s is divided by 7?

Show Spoiler
e

a. 2
b. 3
c. 4
d. 5
e. 6

i would suggest to take num rather than doing it algerabically.

take 10.. when it divided by 7 it will have remainder 3..
So R=10..

S will also B 10..

Square of 10..=100

r2-s..100-10=90..

90 /7 ..u l have remained 6 ..

Hope it helps !

Hi Sanjoo,

In this method, how do we know if R=S?
If R=10, S can be 3 or 10 or 17 etc, isn't it?
If S=3, then r2-s=100-9=91, 91/7 gives a remainder of 0.
If S=10, then as per the calculation, we get a remainder of 6.
Wondering if I missed something here?
Show more

Hi pdavulur,
Please check the highlighted part.
You have subtracted \(r^2-s^2 \)instead of \(r^2-s\)
User avatar
pdavulur
User avatar
Joined: 22 Jun 2023
Last visit: 19 Oct 2023
Posts: 6
Given Kudos: 35
Posts: 6
Kudos: 0
When integer r is divided by 7, the remainder is 3. When 29 Aug 2023, 08:25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thanks Nabneet for calling it out :)

I definitely missed that!
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,962
Own Kudos:
1,117
Posts: 38,962
Kudos: 1,117
When integer r is divided by 7, the remainder is 3. When 07 Oct 2025, 19:46
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
109785 posts
Krunaal
Tuck School Moderator
853 posts