The product of n consecutive integers equals P.

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

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

[spoiler]OA=A[/spoiler]

Source: Magoosh

Since there are at least two integers (given that n ≥ 2), the product of n integers must be even (we have at least one 2 in P). So, Statement I is correct, therefore, Statement II is incorrect.

Statement III is not must be true. Let's take an example: Say, the n consecutive integers are –3, – 2 and – 1; thus, P = –6, not positive.

The correct answer: A

Hope this helps!

-Jay
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Gmat_mission wrote:The product of \(n\) consecutive integers equals \(P\). Which of the following is true for \(n \ge 2?\)

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

[spoiler]OA=A[/spoiler]

Source: Magoosh

If P is the product of at least two consecutive integers, then at least 1 of the integers is even, and thus P must be even, so I is true. Furthermore, since P is even, it cannot be odd, so II is false. We also cannot say for sure whether P is positive. For example, if one of the integers is 0, then P = 0, which is not positive, so III is false.

Answer: A

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

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

[spoiler]OA=A[/spoiler]

Source: Magoosh

If P is the product of at least two consecutive integers, then at least 1 of the integers is even, and thus P must be even, so I is true. Furthermore, since P is even, it cannot be odd, so II is false. We also cannot say for sure whether P is positive. For example, if one of the integers is 0, then P = 0, which is not positive, so III is false.

Answer: A