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When integer r is divided by 7, the remainder is 3. When [#permalink]
 29 Sep 2012, 13:14
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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
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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]
29 Sep 2012, 14:50
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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? a. 2 b. 3 c. 4 d. 5 e. 6 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, 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 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, 23:52
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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? 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]
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
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Re: What is the remainder when r^2 - s is divided by 7? [#permalink]
01 Oct 2012, 06:47
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]
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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Re: When integer r is divided by 7, the remainder is 3. When [#permalink]
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
Brother Karamazov
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Re: When integer r is divided by 7, the remainder is 3. When
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26 Oct 2012, 13:05
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