joannabanana wrote:If p and n are positive integers and 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.
p^2 - n^2 = (p+n)(p-n). So the question can be rewritten as:
What is the remainder when (p+n)(p-n) is divided by 15?
Statement 1:
Tells us nothing about p-n. Insufficient.
Statement 2:
Tells us nothing about p+n. Insufficient.
Statements 1 and 2 together:
The remainder when p+n is divided by 5 is 1. This means that p+n is a (multiple of 5) + 1. Multiples of 5 are 0,5,10,15,20, etc.
So p+n = 1,6,11,16,21,etc.
The remainder when p-n is divided by 3 is 1. This means that p-n is a (multiple of 3) + 1. Multiples of 3 are 0,3,6,9,12, etc.
So p-n = 1,4,7,10,13,etc.
If p+n=11 and p-n=1 so that p=6 and n=5, then (p+n)(p-n) = 11*1 = 11.
11/15 = 0 R11.
If p+n=21 and p-n=1 so that p=11 and n=10, then (p+n)(p-n) = 21*1 = 21.
21/15 = 1 R6.
Since the remainder can take on different values, insufficient.
The correct answer is E.
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