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If P is a set of consecutive integers, is there an even

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by BTGmoderatorDC » Thu Sep 12, 2019 4:55 pm

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If P is a set of consecutive integers, is there an even number of integers in set P?

(1) The sum of the integers in set P is 0.
(2) The product of the integers in set P is 0.

OA A

Source: Princeton Review
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by Jay@ManhattanReview » Thu Sep 12, 2019 9:34 pm
BTGmoderatorDC wrote:If P is a set of consecutive integers, is there an even number of integers in set P?

(1) The sum of the integers in set P is 0.
(2) The product of the integers in set P is 0.

OA A

Source: Princeton Review
Let's take each statement one by one.

(1) The sum of the integers in set P is 0.

Case 1: There is only one integer in the set and that is 0. So, the number of integers in the set is not even. The answer is No.
Case 2: Taking more than one integer.

To make the sum equal to 0 and complying that the integers are consecutive if there is an integer in the set as n, its opposite number, -n, must also be in the set, ensuring the sum equal to 0. Since n and -n lie on the opposite sides of 0, there would be odd numbers of elements in the set. The answer is No.

Unique answer. Sufficient.

(2) The product of the integers in set P is 0.

Case 1: Say there are two, even numbers of elements in the set. They are 0 and 1. The answer is yes.
Case 2: Say there are three, odd numbers of elements in the set. They are 0, 1 and 2. The answer is no.

No unique answer. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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