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If p and n are positive integers and p > n, what is the

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If p and n are positive integers and p > n, what is the [#permalink] New post 23 Sep 2009, 18:44
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If p and n are positive integers and p > n, what is the remainder when p^2 - n^2 is devided by 15?

a) The reminder when p + n is divided by 5 is 1.
b) The reminder when p - n is divided by 3 is 1.


¿¿??
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Aeros
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Re: Reminders [#permalink] New post 24 Sep 2009, 06:52
Quote:
If p and n are positive integers and p > n, what is the remainder when p^2 - n^2 is devided by 15?

a) The reminder when p + n is divided by 5 is 1.
b) The reminder when p - n is divided by 3 is 1.


¿¿??


a): p+n/5 has a remainder of 1. Therefore, p+n = 6 or p+n+11 or p+n = 16 (so on and so forth)
Let's assume p + n = 6
Substitute 5 for p and 1 for n (because P>N)
Also, substitute 4 for p and 2 for n
Take p=5 and n = 1
5^2 - 1^2 = 24 and 24/15 has a remainder of 9

Take p = 4 and n = 2
4^2 - 2^2 = 16-4 = 12 and 12/15 has a remainder of 12
Therefore A is insufficient

b) p-n/3 has a remainder of 1 so p-n = 4 or p-n =7 or p-n = 11
If p-n = 4, p-n = 5-1 or 6-2 and so on
If p = 5 and n = 1 then
5^2 - 1^2 = 24 and 24/15 has a remainder of 9
If p = 6 and n = 2 then
6^2 - 2^2 = 32 and 32/15 has a remainder of 2
Therefor B is insufficient

Take both together:
Well you can assume P = 5 and n = 1 (because 5-1 = 4 and 5+1 = 6; using the information from above)
You already worked the math and figured that the remainder would be 9

However, you can have P = 9 and N = 2
9+2 = 11 (which satisfies part A) and 9 -2 = 7 (which satisfies part B)
9^2 - 2^2 = 81 - 4 =77
77/15 has a remainder of 2

Therefore, I'm getting the answer is E
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Re: Reminders [#permalink] New post 24 Sep 2009, 07:04
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aeros232 wrote:
If p and n are positive integers and p > n, what is the remainder when p^2 - n^2 is devided by 15?

a) The reminder when p + n is divided by 5 is 1.
b) The reminder when p - n is divided by 3 is 1.


¿¿??


Hi,

p^2 - n^2 = (p+n)(p-n) (I)

FOR (A):
p+n= 5k+1 (For some, K is integer) => (p+n)(p-n)=5x(p-n)xK + (p-n) BUT We dont know what value is (p-n). (INSUFFI)

FOR (B)
p-n= 3K'+1 (For some, K' is integer) => (p-n)(p+n)=3x(p+n)xK' + (p+n) BUT We dont know what value is (p+n). (INSUFFI)

FOR (A) and (B),

(p+n)(p-n)=(5k+1)(3k'+1)= 15xKxK'+5k+3K'+1 => We dont the value for: 5k+3K'+1??

Finally,

Answer = E

Cheers!
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Re: Reminders [#permalink] New post 26 Sep 2009, 09:31
I too go with statement E. Both statements are insufficient.
Re: Reminders   [#permalink] 26 Sep 2009, 09:31
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