Is the sum of 6 integers odd?

[VJesus12]

Is the sum of 6 integers odd?

1) The product of four largest integers is odd, and the product of two smallest integers is even

2) the sum of two smallest integers is odd, and the sum of four largest integers is even

The OA is B.

Why statement 1 is not sufficient? Can any expert explain it step by step? Thanks.

[Jay@ManhattanReview]

Is the sum of 6 integers odd?

1) The product of four largest integers is odd, and the product of two smallest integers is even

2) the sum of two smallest integers is odd, and the sum of four largest integers is even

The OA is B.

Why statement 1 is not sufficient? Can any expert explain it step by step? Thanks.

The sum of 6 integers is odd if one, three, or five numbers of integers are odd.

Question rephrased: Are there one, three, or five numbers of odd integers?

1) The product of four largest integers is odd, and the product of two smallest integers is even.

(i) The product of four largest integers is odd implies that all the four integers are odd.
(ii) The product of two smallest integers is even implies that either both are even or only one is even and the other is odd.

Thus, the number of odd integers can be four or five. No unique answer. Insufficient.

Hope this helps!

-Jay
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