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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions