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Is |A| + |B| is even? 1) |A|-|B| is even 2) |A||B| is even

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Himalayan
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Is |A| + |B| is even? 1) |A|-|B| is even 2) |A||B| is even [#permalink] New post   11 Jul 2007, 23:09
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Is |A| + |B| is even?

1) |A|-|B| is even
2) |A||B| is even



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Re: Is |A| + |B| is even? 1) |A|-|B| is even 2) |A||B| is even [#permalink] New post   11 Jul 2007, 23:30
Statement 1 by itself is insufficient since:

|A| = 1/2

|B| = 1/2

|A|-|B| = |1/2|-|1/2| = 0 (even number)

|1/2|+|1/2| = 1 (odd number)

statement 2

|1/2|*|1/2| = 1/4 (not an even number)

hence the answer is (C)

:-D
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Re: Is |A| + |B| is even? 1) |A|-|B| is even 2) |A||B| is even [#permalink] New post   12 Jul 2007, 06:09
|A| - |B| even isn't sufficient, good counter example in the above post.

|A||B| = even => that either |A| is even or |B| is even or both are Even.

Statement 2 itself isn't sufficient since A=1,B=2 => |A||B| =2 but not |A| + |B|

Combining both conditions though implies that both A and B have to be even numbers and Therefore (C)
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Re: Is |A| + |B| is even? 1) |A|-|B| is even 2) |A||B| is even [#permalink] New post   12 Jul 2007, 10:41
I agree with the OA but not with the example KillerSquirrel provided for Stmt 1.

0 is neither even nor odd. A better example would be A = 2.25 B = .25

A- B is even.But A + B is not.
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Re: Is |A| + |B| is even? 1) |A|-|B| is even 2) |A||B| is even [#permalink] New post   12 Jul 2007, 11:05
dahcrap wrote:
I agree with the OA but not with the example KillerSquirrel provided for Stmt 1.

0 is neither even nor odd. A better example would be A = 2.25 B = .25

A- B is even.But A + B is not.


As far as I know, zero (0) is an even number.
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Re: Is |A| + |B| is even? 1) |A|-|B| is even 2) |A||B| is even [#permalink] New post   12 Jul 2007, 11:11
Wait a minute... let me know where I went wrong.

1) if a=v2 and b=v2 then a-b=0 which is even (OG defines 0 as even pg.108)

2) if a=v2 and b=v2 then a*b=2 which is even

Using those numbers in the original equation v2 + v2 does not equal an even number, it equals a decimal. So E would have to be the answer. Right??
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Re: Is |A| + |B| is even? 1) |A|-|B| is even 2) |A||B| is even [#permalink] New post   12 Jul 2007, 12:07
dahcrap wrote:
0 is neither even nor odd.



dahcrap, 0 is always even.



logical reasoning:

even = even - 2
odd = odd - 2

odd - 2 =/= 0, therefore 0 is even.
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Re: Is |A| + |B| is even? 1) |A|-|B| is even 2) |A||B| is even [#permalink] New post   12 Jul 2007, 12:25
Himalayan wrote:
dahcrap wrote:
0 is neither even nor odd.



dahcrap, 0 is always even.



logical reasoning:

even = even - 2
odd = odd - 2

odd - 2 =/= 0, therefore 0 is even.


I need to remember this. Then in this case E has to be the OA
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Re: Is |A| + |B| is even? 1) |A|-|B| is even 2) |A||B| is even [#permalink] New post   12 Jul 2007, 12:59
dahcrap wrote:
Himalayan wrote:
dahcrap wrote:
0 is neither even nor odd.



dahcrap, 0 is always even.



logical reasoning:

even = even - 2
odd = odd - 2

odd - 2 =/= 0, therefore 0 is even.


I need to remember this. Then in this case E has to be the OA


For sure. I think I proved that in the above post (take a and b to both equal radical 2). Can someone verify?
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Re: Is |A| + |B| is even? 1) |A|-|B| is even 2) |A||B| is even [#permalink] New post   12 Jul 2007, 15:38
Statement 1) sqrt(2)-sqrt(2)= 0
is even

Statement 2) sqrt(2)*sqrt(2)= 2
is even

however sqrt(2)+sqrt(2)= 2sqrt(2)
and is not even

hence E
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Re: Is |A| + |B| is even? 1) |A|-|B| is even 2) |A||B| is even [#permalink] New post   13 Jul 2007, 21:55
Yes ! I see my mistake - nice reply baer

the answer is indeed (E)

good discussion all


:-D



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Re: Is |A| + |B| is even? 1) |A|-|B| is even 2) |A||B| is even [#permalink]
13 Jul 2007, 21:55
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