When integer r is divided by 7, the remainder is 3. When : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 23 Feb 2017, 09:34

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# When integer r is divided by 7, the remainder is 3. When

Author Message
TAGS:

### Hide Tags

Intern
Joined: 04 Sep 2009
Posts: 43
Followers: 1

Kudos [?]: 57 [0], given: 9

When integer r is divided by 7, the remainder is 3. When [#permalink]

### Show Tags

29 Sep 2012, 12:14
1
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:00) correct 21% (00:52) wrong based on 109 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA

_________________

Aeros
"Why are you trying so hard to fit in when you were born to stand out?"
"Do or do not. There is no 'try'..."

Last edited by Bunuel on 30 Sep 2012, 03:39, edited 2 times in total.
Renamed the topic and edited the question.
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 101

Kudos [?]: 910 [1] , given: 43

Re: What is the remainder when r^2 < s is divided by 7? [#permalink]

### Show Tags

29 Sep 2012, 13:50
1
KUDOS
aeros232 wrote:
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?

[Reveal] 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.

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Senior Manager
Joined: 06 Aug 2011
Posts: 405
Followers: 2

Kudos [?]: 197 [1] , given: 82

Re: What is the remainder when r^2 - s is divided by 7? [#permalink]

### Show Tags

29 Sep 2012, 22:52
1
KUDOS
aeros232 wrote:
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?

[Reveal] 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 !
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Math Expert
Joined: 02 Sep 2009
Posts: 37099
Followers: 7249

Kudos [?]: 96416 [1] , given: 10750

Re: What is the remainder when r^2 - s is divided by 7? [#permalink]

### Show Tags

01 Oct 2012, 05:47
1
KUDOS
Expert's post
sanjoo wrote:
aeros232 wrote:
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?

[Reveal] 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.
_________________
Intern
Joined: 04 Sep 2009
Posts: 43
Followers: 1

Kudos [?]: 57 [0], given: 9

Re: What is the remainder when r^2 < s is divided by 7? [#permalink]

### Show Tags

29 Sep 2012, 14:01
EvaJager wrote:
aeros232 wrote:
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?

[Reveal] 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.

Yes, you are right!!! And by the way, excellent explanation, thanks!!
_________________

Aeros
"Why are you trying so hard to fit in when you were born to stand out?"
"Do or do not. There is no 'try'..."

Intern
Joined: 26 Sep 2012
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: What is the remainder when r^2 - s is divided by 7? [#permalink]

### Show Tags

29 Sep 2012, 23:06
aeros232 wrote:
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?

[Reveal] Spoiler:
e

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

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
Senior Manager
Joined: 06 Aug 2011
Posts: 405
Followers: 2

Kudos [?]: 197 [0], given: 82

Re: When integer r is divided by 7, the remainder is 3. When [#permalink]

### Show Tags

01 Oct 2012, 08:23
Bunuel wrote:
sanjoo wrote:
aeros232 wrote:
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?

[Reveal] 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.

Thanks for kudos ..MATH GURU....
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Intern
Joined: 11 Jul 2012
Posts: 46
Followers: 0

Kudos [?]: 5 [0], given: 0

Re: When integer r is divided by 7, the remainder is 3. When [#permalink]

### Show Tags

26 Oct 2012, 12:05
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
Re: When integer r is divided by 7, the remainder is 3. When   [#permalink] 26 Oct 2012, 12:05
Similar topics Replies Last post
Similar
Topics:
7 When a positive integer is divided by 4, the remainder is r; when divi 6 28 Dec 2016, 00:22
1 When integer x is divided by 5 the remainder is 3 and when x is divide 3 05 Dec 2016, 01:23
When the positive integer A is divided by 5 and 7, the remainder is 3 2 18 Oct 2016, 14:20
44 If the remainder is 7 when positive integer n is divided by 14 06 Mar 2012, 22:28
4 When the integer k is divided by 12, the remainder is 3. 3 06 Jul 2008, 20:25
Display posts from previous: Sort by