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# a, b, and c are integers. Is a+b+c even? (1) a+b is even (2)

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a, b, and c are integers. Is a+b+c even? (1) a+b is even (2) [#permalink]

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07 Aug 2003, 01:26
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a, b, and c are integers. Is a+b+c even?

(1) a+b is even
(2) a+c is even
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07 Aug 2003, 02:10
One vote for E.

Solution:

Statement one: insufficient. If a+b is even, ether a and b are both even, or both odd. In the first case c can be odd and even.

Statement two: insufficient. See statement one.

Combine: insufficient. Let us add two statements together. (Do not forget: even+even=even). We get 2a+b+c = even. Substitute even a,b and c into the combined equation => 2a+b+c=even (original a+b+c - even). Now try a,b,c - odd => 2a+b+c = is still even, however, the original statement is odd. Thus, the answer is E.

- Stolyar?
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KL

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07 Aug 2003, 04:04
stolyar wrote:
a, b, and c are integers. Is a+b+c even?

(1) a+b is even
(2) a+c is even

We know that

even+even=even and odd+odd=even
AND
even+even+even=even and odd+odd+even=even

Now from (1) we know that a and b are both odd or both even

From (2) we know that a and c are both odd or both even

Combining the two we know that a, b and c are of the same kind - odd or even.

In this case, a+b+c can be even only if all three are even - which we do not know.

Hence I choose E
Re: DS: EVEN   [#permalink] 07 Aug 2003, 04:04
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