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

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If p and n are positive integers p >n , what is the [#permalink]  11 Oct 2008, 07:40
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If p and n are positive integers p >n , what is the remainder when p^2-n^2 is divided by 15

(1) The remainder when p+n is divided by 5 is 1
(2) The remainder when p-n is divided by 3 is 1
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Re: DS : p and n are positive integers [#permalink]  11 Oct 2008, 07:50
IMO C:

Please confirm ,i will give explanation after confirmation

(p-n)(p+n) is divisible by 15 ( 3 and 5 )or not..

A: it says remainder p+n is divided by 5 is 1.
7 + 4 =11 /5 ->reminder = 1 p-n= 3
8+4 = 11 /5-> reminder =1 p-n = 5

So A is not suff.

B:
remainder p-n is divided by 3 is 1
5 -4 = 1/3->reminder = 1 p+n = 9 divisible by 3
8-4 =1/3->reminder = 1 p+n=12 divisible by 3.
12-2=10/3->reminder=1 p+n= 14 not divisible by 3 or 5 but p-n is divisible by 5
So B is not suff.

A+ B
yes its suff. check it
Thanks
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Re: DS : p and n are positive integers [#permalink]  11 Oct 2008, 09:37
IMO E.

Explanation below:

The questions ask for the remainder when (p^2-n^2) divided by 15 ~ (p-n)(p+n):15

(1): p+n=5i+1 -> not suf.

(2): p-n=3m+1 -> not suf.

(1) and (2) combined: (p-n)(p+n)=(5i+1)(3m+1)=15im+5i+3m+1 -> not suf. to determine the remainder 5i+3m+1

E it goes.
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Re: DS : p and n are positive integers [#permalink]  11 Oct 2008, 09:49
I will go with madhusudan. For me ans is E)
Just take a exapmle

24/15 = 6x4/5x3 , when 6 divided by 5 than remainder is 1 & now when 4 divided by 3 again remainder is 1, But 24/15 has remainder 9
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Re: DS : p and n are positive integers [#permalink]  11 Oct 2008, 12:22
I get E as well..

(p+n)(p-n)=5K+r

P+N=5K+1

well p+n=6 then p-n=5-1=4...remainder would be 4..

p+n=16, then p-n=10-6=4 remainder would be 4..

if p+n=11, p-n=1 (i.e. 6-5) remainder would be 1..
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Re: DS : p and n are positive integers [#permalink]  11 Oct 2008, 13:30
E

Going with everybody's explanation:
Statement 1: Insufficient
Statement 2: Insufficient

Together :
If p+n = 6, you have to pick, p-n = 4 --> p=5, n=1
then,
R = 9

If p+n = 11, you have to pick p-n = 7 -->p=9, n= 2
then,
R = 2
Insufficient
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Re: DS : p and n are positive integers [#permalink]  12 Oct 2008, 22:20
I still dont understand, so the result is E or C
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Re: DS : p and n are positive integers [#permalink]  12 Oct 2008, 22:49
mimi28 wrote:
I still dont understand, so the result is E or C

Check the explanation from vishalgc.
Re: DS : p and n are positive integers   [#permalink] 12 Oct 2008, 22:49
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