2015 Countdown Problem #5: Multiplication Madness
The product of 2015 positive odd numbers multiplied by the product of 2016 positive even numbers multiplied by the product of 2017 negative odd numbers multiplied by the product of 2018 negative odd numbers is...
This problem is part of the set 2015 Countdown Problems .
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Each product is a factor of the final product.
First we look at if the answer is positive or negative. Positive factors always have a positive product. The first two products are positive. An odd number of negative factors have a negative product, and the reverse is also true. Hence 2017 negative numbers have a negative product and 2018 negative numbers have a positive product. Since an odd number of negative factors have a negative product, and there is only one negative factor, the answer must be negative.
Then we find out if the answer is odd or even. Out of the four products, three are odd and one is even. Since one factor is even, the answer must be even.
Hence the answer is a negative even number.
Sorry if I used too many words.