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# If a and b are positive integers (a > b), is a^2 - b^2

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Senior Manager
Joined: 05 Oct 2008
Posts: 263
If a and b are positive integers (a > b), is a^2 - b^2 [#permalink]

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07 Nov 2008, 07:36
If a and b are positive integers (a > b), is a^2 - b^2 divisible by 4?

1. a = b + 2
2. a and b are odd

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Manager
Joined: 05 Jul 2008
Posts: 134
GMAT 2: 740 Q51 V38

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07 Nov 2008, 07:47
study wrote:
If a and b are positive integers (a > b), is a^2 - b^2 divisible by 4?

1. a = b + 2
2. a and b are odd

a2-b2= (a-b)(a+b)

1. a = b + 2 => a-b and a+b are even
Enough
2. a and b are odd => a-b and a+b are even
Enough
So D
VP
Joined: 05 Jul 2008
Posts: 1367

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07 Nov 2008, 09:13
study wrote:
If a and b are positive integers (a > b), is a^2 - b^2 divisible by 4?

1. a = b + 2
2. a and b are odd

D

Q is asking whether (a-b) (a+b) is divisible by 4, given a,b >0 and int

a= b+2 means it comes down to 2 (2b+2) which is 4 (b+1) . Yes divisible by 4

a and b are odd. Both sum and difference are even. Two even numbers. That means there must be atleast two 2's . Hence product is divisible by 4
Manager
Joined: 11 Apr 2008
Posts: 198

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07 Nov 2008, 12:43
Yea the ans should be D
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Joined: 30 Apr 2008
Posts: 1850
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07 Nov 2008, 13:00
Did anyone else use number picking?

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Re: No. Properties   [#permalink] 07 Nov 2008, 13:00
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# If a and b are positive integers (a > b), is a^2 - b^2

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