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

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25% (low)

Question Stats:

81% (01:46) correct
19% (01:00) wrong based on 81 sessions

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?

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

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]
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?

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]
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?

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

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

Re: What is the remainder when r^2 - s is divided by 7? [#permalink]
01 Oct 2012, 05:47

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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?

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. _________________

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

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 !