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# If A & B are positive integers, is a^2 + b^2 divisible

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CEO
Joined: 21 Jan 2007
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If A & B are positive integers, is a^2 + b^2 divisible  [#permalink]

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15 Nov 2007, 02:53
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If A & B are positive integers, is a^2 + b^2 divisible by 5?

1. 2AB is divisible by 5
2. A-B is divisible by 5

Can someone walk me thru the solution

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Intern
Joined: 14 Nov 2007
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15 Nov 2007, 03:32
bmwhype2 wrote:
If A & B are positive integers, is a^2 + b^2 divisible by 5?

1. 2AB is divisible by 5
2. A-B is divisible by 5

Can someone walk me thru the solution

It seems like E is here. I just took 2 examples :

1) 7 and 6 : 7^2+6^2 = 85 which is divisible by 5
On the other hand 7-6 is not divisible by 5 and 7*6*2 is not divisible by 5

2) the other story is 10 and 5 10^2 + 5^2 = 125 which is divisible by 5.
10-5 anf 10*5*2 are both divisible by 5.

Therefore - E
Director
Joined: 09 Aug 2006
Posts: 745

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15 Nov 2007, 07:13
bmwhype2 wrote:
If A & B are positive integers, is a^2 + b^2 divisible by 5?

1. 2AB is divisible by 5
2. A-B is divisible by 5

Can someone walk me thru the solution

C.

Stat 1: Tells us that at least one of A and B is divisible by 5. If A = 10 and B = 5 then answer to stem is yes. If A = 10 and B = 2 then answer to stem is no. Insuff.

Stat 2: Tells us that A-B is a multiple of 5 but says nothing about A or B. If A = 10 & B = 5 answer to stem is yes. If A = 12 & B = 7 answer to stem is no. Insuff.

Together: Since A (or B) has to be a multiple of 5 according to stat 1, B (or A) has to be a multiple of 5 as well for stat 2 to be true. (Multiple of 5)^2 + (Multiple of 5)^2 has to be divisible by 5. Suff.
Manager
Joined: 21 Jun 2007
Posts: 141
Schools: UCLA Anderson School of Mgmt (FEMBA Class of 2013)
WE 1: 7.5 years in Engg. Consulting

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15 Nov 2007, 07:56
First, I will reword the qn in to

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

Statement 1: 2ab is divisible by 5, does not help much unless the first part is divisible by 5, so not sufficient.

Statement 2: Says a-b is divisible by 5, so (a-b)^ 2 will be divisible by 5, but as Statement 1 unless 2ab is also divisible by 5, the whole expression will not be, so not sufficient.

Both statement combined, we can say the expression is divisible by 5.

Senior Manager
Joined: 13 Dec 2006
Posts: 492
Location: Indonesia

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15 Nov 2007, 08:03
Dear Soomodh,

you have calculated correctly but in that case answer will be C and not D.

Amar
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Re: If A & B are positive integers, is a^2 + b^2 divisible  [#permalink]

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29 Sep 2017, 15:27
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Re: If A & B are positive integers, is a^2 + b^2 divisible &nbs [#permalink] 29 Sep 2017, 15:27
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