Question rephrased: What is the remainder when (p+n)(p-n) is divided by 15?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
Statement 1: No information about p+n. INSUFFICIENT.
Statement 2: No information about p-n. INSUFFICIENT.
Statements 1 and 2 combined:
The remainder when p+n is divided by 5 is 1.
This statement implies the following:
p+n = 5k+1, where k≥0.
Thus, p+n = 1,6,11,16,21...
The remainder when p-n is divided by 3 is 1.
This statement implies the following:
p-n = 3m+1, where m≥0.
Thus, p-n = 1,4,7,10,13...
Case 1: p+n=11 and p-n=1
Adding the two equations:
2p=12
p=6, implying than n=5.
(p+n)(p-n)/15 = (11*1)/15 = 0 R11.
Case 2: p+n=21 and p-n=1
Adding the two equations:
2p=22
p=11, implying than n=10.
(p+n)(p-n)/15 = (21*1)/15 = 1 R6.
Since different remainders are possible, INSUFFICIENT.
The correct answer is E.
