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Algebra Difficulty 2.4 Junior Find the answer

Suppose that dd is an odd integer and ee is an even integer. How many of the following expressions are equal to an odd integer? d+d,(e+e)imesd,dimesd,dimes(e+d)d+d, (e+e) imes d, d imes d, d imes(e+d)

A number or a short expression. Spacing and $ signs are ignored.

Solution

Since dd is an odd integer, then d+dd+d is even and dimesdd imes d is odd. Since ee is an even integer, then e+ee+e is even, which means that (e+e)imesd(e+e) imes d is even. Also, e+de+d is odd, which means that dimes(e+d)d imes(e+d) is odd. Thus, 2 of the 4 expressions are equal to an odd integer.

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