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

Question

Given two positive integers A and B such that A > B, what is the remainder when the square of B is subtracted from the square of A and then divided by 15?

(1) When the sum of A and B is divided by 5, the remainder is 1

(2) When B is subtracted from A and then divided by 3, the remainder is 1.

Akash720 · Answer

Given:
When (B^2 - A^2)/15 find remainder

B^2 - A^2 = (B+A)(B-A)

Statement 1:
When (B+A)/5 Remainder = 1. Insufficient as we don't have remainder for B-A
Statement 2:
When (A-B)/3 Remainder = 1. Insufficient as we don't have remainder for B-A and B+A

1&2:
Insufficient
We don't have the remainder when B-A is divided by 3.

rahulkashyap · Answer

with A we have a+b = 5k+1
with B we have a - b = 3m+1

multiplying the 2 we have: (15km)+ 5k+3m+1

ans should be e

chetan2u · Answer

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

sejm · Answer

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?

gurmukh · Answer

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

Posted from my mobile device

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

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