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

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Joined: 04 Sep 2009
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When integer r is divided by 7, the remainder is 3. When  [#permalink]

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Updated on: 30 Sep 2012, 04:39
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79% (00:57) correct 21% (01:02) wrong based on 157 sessions

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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

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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'..."

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

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29 Sep 2012, 14:50
1
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?

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.

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Intern
Joined: 04 Sep 2009
Posts: 41
Re: What is the remainder when r^2 < s is divided by 7?  [#permalink]

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29 Sep 2012, 15:01
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?

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!!
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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'..."

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Posts: 356
Re: What is the remainder when r^2 - s is divided by 7?  [#permalink]

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29 Sep 2012, 23:52
2
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?

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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Intern
Joined: 26 Sep 2012
Posts: 1
Re: What is the remainder when r^2 - s is divided by 7?  [#permalink]

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30 Sep 2012, 00:06
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?

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
Math Expert
Joined: 02 Sep 2009
Posts: 48109
Re: What is the remainder when r^2 - s is divided by 7?  [#permalink]

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01 Oct 2012, 06:47
1
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?

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

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01 Oct 2012, 09:23
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?

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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Intern
Joined: 11 Jul 2012
Posts: 41
Re: When integer r is divided by 7, the remainder is 3. When  [#permalink]

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26 Oct 2012, 13:05
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
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When integer r is divided by 7, the remainder is 3. When  [#permalink]

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08 Dec 2017, 13:03
Bunuel wrote:
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
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Joined: 02 Sep 2009
Posts: 48109
Re: When integer r is divided by 7, the remainder is 3. When  [#permalink]

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08 Dec 2017, 22:44
gracie wrote:
Bunuel wrote:
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

If r = 3 and s = 10, then r^2 - s = -1. The remainder when -1 id divided by 7 is also 6.
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Re: When integer r is divided by 7, the remainder is 3. When &nbs [#permalink] 08 Dec 2017, 22:44
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