I'm happy to help with this.
Prompt:
Is the smallest of nine consecutive integers an even number?
So, we have nine consecutive integers, and we want to know the starting point.
Statement #1:
The product of the integers is even.
This is not so helpful. You see, no matter how many odds you multiply together, all you need is one even number, and the whole product is even. Here, if we have consecutive integers, every other one will be even, so we will have plenty of even numbers in the product, so the product will definitely be even, regardless of the starting point. This is completely useless for answering the prompt. Statement #1, by itself, is
insufficient.
Statement #2:
The sum of the integers is zero.
This is interesting. In order to have a sum of zeros, the string of consecutive numbers must be symmetrically arranged around zero, so there are an equal number of positive and negatives. That means the series of consecutive numbers has to be
-4, -3, -2, -1, 0, 1, 2, 3, 4
We know the series, so we can see that the smallest, -4, is even. We can give a definitive answer to the prompt. Statement #2, by itself, is
sufficient.
Answer =
B
Here's another DS about consecutive integers:
https://gmat.magoosh.com/questions/943
When you submit your answer, the next page will have a complete video explanation. At Magoosh, we have 800+ GMAT questions, each with its own video explanation. We also have 200+ lesson videos, including lessons on strategies for DS questions like this one. We have a sale ending Thursday, so now's a particularly good time to check us out.
Does all this make sense? Let me know if you have any questions?
Mike
