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

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When integer r is divided by 7, the remainder is 3. When [#permalink] New post 29 Sep 2012, 12:14
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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

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Last edited by Bunuel on 30 Sep 2012, 03:39, edited 2 times in total.
Renamed the topic and edited the question.
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Re: What is the remainder when r^2 < s is divided by 7? [#permalink] New post 29 Sep 2012, 13:50
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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.

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

Answer E.


Yes, you are right!!! And by the way, excellent explanation, thanks!!
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Re: What is the remainder when r^2 - s is divided by 7? [#permalink] New post 29 Sep 2012, 22:52
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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 !
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Re: What is the remainder when r^2 - s is divided by 7? [#permalink] New post 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
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Re: What is the remainder when r^2 - s is divided by 7? [#permalink] New post 01 Oct 2012, 05:47
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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.
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Senior Manager
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Re: When integer r is divided by 7, the remainder is 3. When [#permalink] New post 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..:)..
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Re: When integer r is divided by 7, the remainder is 3. When [#permalink] New post 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
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