Given two positive integers A and B such that A > B, what is the remai

\(a^2-b^2=(a-b)(a+b)\)

Individually they are clearly insufficient..

So let's see combined...
1) \(a+b=5x+1\)
2) \(a-b=3y+1\)

So \((a-b)(a+b)=(5x+1)(3y+1)=15xy+5x+3y+1\)
We have to check for 5x+3y+1, as 15xy is divisible by 15.....

1) If x is multiple of 3 and y a multiple of 5, remainder will be 1...
Say a is 31 and b is 15... a-b=16=3*5+1....a+b=46=3*15+1
2) otherwise remainder can be anything
Say a is 14 and b is 7.. \(a-b=14-7=7=3*2+1 ....a+b=14+7=21=4*5+1\)
Remainder =\(\frac{7*21}{15}=147\) so remainder=12
Insufficient

E

Can someone help me understand this question and how I solved it incorrectly? Here is what I did:

The question is asking what is remainder when (A^2 - B^2)/15.

So what is the remainder when (A+B)(A-B)/15?

1. We are given (A+B)/5 = R1. This is insufficient because we don't know what (A-B) =
2. We are given (A-B)/3 = R1. This is insufficient because we don't know what (A+B) =
Together: (A+B)(A-B)/15 -> Let's split this remainders. (A+B)/15 = R1 (15 is a multiple of 5 so remainder will be 1) (A-B)/15 = R1 (15 is a multiple of 3 so remainder will be 1) Thus we can calculate the value, and both statements are sufficient.

What did I do wrong? Why is the answer E?

6/5 gives a remainder 1 but that does not mean 6/15 will also give me a remainder 1.

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