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Thoughts on this Question?

by yumi2012 » Sun Aug 04, 2013 8:03 pm
This Q is found on page 41 of the MGMAT guide book "Number Properties"

Q: If c,d, and e are consecutive integers, is cde odd or even?

My answer: "cannot be determined".. because there's no mention of any of integers not being "0" so I thought if any of them is 0 then the product is neither even nor odd.

However, the answer from MGMAT book is "even"... Any thoughts?
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by [email protected] » Mon Aug 05, 2013 12:11 am
Hi yumi2012,

0 is an even number and it's considered a "null" value (neither positive nor negative).

If you have 3 consecutive integers, then the product MUST be even. Here's why:

Either your first integer is even or it's odd.
If it's even, then the 3 terms are: (even)(odd)(even) and the product is even. e.g.. (2)(3)(4) = 24
Or it's odd, then the 3 terms are: (odd)(even)(odd) and the product is even. e.g. (-1)(0(1) = 0

DON'T CONFUSE even/odd with positive/negative/zero

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by Brent@GMATPrepNow » Mon Aug 05, 2013 7:44 am
I should add that there's a rule that says . . .

The product of n consecutive integers is divisible by n, n-1, n-2,..., and 1.

So, for example, the product of any 6 consecutive integers will be divisible by 6, 5, 4, 3, 2 and 1 (of course, the product can be divisible by other numbers as well)

So, in your question, we have 3 consecutive integers (c, d and e). So, the product cde must be divisible 3, 2, and 1
If it's divisible by 2, then it's definitely even.

Cheers,
Brent
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