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

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Math Expert
Joined: 02 Sep 2009
Posts: 56303
Given two positive integers A and B such that A > B, what is the remai  [#permalink]

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19 Jul 2018, 00:00
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95% (hard)

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36% (02:49) correct 64% (02:28) wrong based on 73 sessions

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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.

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Re: Given two positive integers A and B such that A > B, what is the remai  [#permalink]

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19 Jul 2018, 02:25
Bunuel wrote:
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.

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.
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Re: Given two positive integers A and B such that A > B, what is the remai  [#permalink]

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19 Jul 2018, 02:48
Bunuel wrote:
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.

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
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Posts: 7764
Re: Given two positive integers A and B such that A > B, what is the remai  [#permalink]

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19 Jul 2018, 03:13
1
Bunuel wrote:
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.

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
So we have to check for 5x+3y+1....
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 =7*21/15=147 so remainder=12
Insufficient

E
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Re: Given two positive integers A and B such that A > B, what is the remai   [#permalink] 19 Jul 2018, 03:13
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