Help with remainder question

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capnx
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Topic: Help with remainder question
PostThu Nov 19, 2009 4:55 pm
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1st Q:
If n is a positive integer and r is the remainder when (n-1)(n+1) is divided by 24, what is the value of r?
1) n is not divisible by 2
2) n is not divisible by 3

2nd Q:
If r is the remainder when integer n is divided by 7, what is the value of r?
1) The remainder is an odd number when n is divided by 21
2) The remainder is 3 when n is divided by 28

Thanks for your explanation
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adamsmith2009
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PostThu Nov 19, 2009 5:31 pm
1st Q:
C

A) n = 3,5,7,9,11,13. If that's divided by 24 you'll get different answers so not sufficient
B) n = 1,2,4,7,10,13. If that's divided by 24 you'll get different answers so not sufficient

What's common in both is 7,13, etc. You'll notice that if you take n+1 and n-1 in both - (6)(8) and (12)(14) they both have a factor of 24 so there won't be any remainder. Sufficient.

2nd Q:
B

A) n = 22, 24, 26, 28, 30. If that's divided by 7 you'll get different answers so not sufficient
B) n = 31, 59, 87. If that's divided by 7 you'll get R=3 for all so sufficient.
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palvarez
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PostThu Nov 19, 2009 9:12 pm
1. what is n^2 (mod 24), we need n^2 (mod 8) and n^2 (3)

1. n = 1 (mod 2)
n = 1,3, 5, 7 (mod 8)
n^2 = 1 (mod 8)
we need n^2 (mod 3). Insuff

2. n = 1 or 2 (mod 3)
n^2 = 1 (mod 3). We need n^2(mod 8). Insuff

Combined , n^2 = 1 (mod 8). Sufficient.


2. what is n (mod 7)

1. n = 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 (mod 21)
n = 1, 3, 5, 0, 2, 4, 6,1,3,5 (mod 7) Insufficient

2. n = 3 (mod 28)
n = 3 (mod 7) Sufficient. B is the answer
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capnx
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PostFri Nov 20, 2009 5:29 pm
thanks guys... sorry I didn't understand any of that mod stuff, lol.
adam's solutions was pretty clear.

palv, are there any online websites that shows how to do the mod calculations?
thanks
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Willy
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PostFri Nov 20, 2009 9:38 pm
What is this modulo stuff...?

palvarez wrote:
1. what is n^2 (mod 24), we need n^2 (mod 8) and n^2 (3)

1. n = 1 (mod 2)
n = 1,3, 5, 7 (mod 8)
n^2 = 1 (mod 8)
we need n^2 (mod 3). Insuff

2. n = 1 or 2 (mod 3)
n^2 = 1 (mod 3). We need n^2(mod 8). Insuff

Combined , n^2 = 1 (mod 8). Sufficient.


2. what is n (mod 7)

1. n = 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 (mod 21)
n = 1, 3, 5, 0, 2, 4, 6,1,3,5 (mod 7) Insufficient

2. n = 3 (mod 28)
n = 3 (mod 7) Sufficient. B is the answer
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