The product of \(n\) consecutive integers equals \(P\).

AAPL wrote:Magoosh

The product of \(n\) consecutive integers equals \(P\). Which of the following is true for \(n \geq 2\)?

I. \(P\) is an even number.
II. \(P\) is an odd number.
III. \(P\) is positive.

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

OA A

Given that \(n \geq 2\), there are at least two consecutive integers. Since every other integer is even and the product of odd and even integer is even, the product of \(n\) consecutive integers is even. So Statement 1 is true; thus, Statement II is false.

Statement III is not must be true. Let's take an example: Say the consecutive integers are 0 and 1. thus, P = 0*1 = 0, not positive.

The correct answer: A

Hope this helps!

-Jay
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AAPL wrote:Magoosh

The product of \(n\) consecutive integers equals \(P\). Which of the following is true for \(n \geq 2\)?

I. \(P\) is an even number.
II. \(P\) is an odd number.
III. \(P\) is positive.

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

OA A

If n is 2, we could have the integers 1 and 2, for a product of 2.

If n is 3, we could have the integers 1, 2, and 3, for a product of 6, or the integers -1, -2, and -3, for a product of -6.

Thus, we see that only I is true.

Answer: A