GMATJudoka wrote:
Ex. 3: -2, -1, 0, 1; Product is 2; insuff.
The product here is 0, not 2, so that's why your calculations led you to an incorrect answer.
In general, the product of n consecutive integers is always divisible by n!, so here, the product of our 4 consecutive integers is automatically divisible by 4! = 24, and in particular is divisible by 3, so Statement 1 is sufficient. There is no reason to consider zero separately.
There are two posts above that carry an 'Expert' tag that might be misleading, so to clarify:
- one post says "zero is divisible by any integer", which is definitely true if you rephrase it to say "zero is divisible by any
positive integer", but is only true, as written, if you use a definition of divisibility that is not universally accepted: by some definitions, zero is divisible by zero, and by some definitions, zero is not divisible by zero. For GMAT purposes, it's best just to think: "you can never divide by zero, so nothing is divisible by zero", though that's not an issue you'll really ever need to worry about regardless.
- another post says "don't be surprised if this exact issue shows up... on test day." I'm not even sure what that means, but there is no reason whatsoever to be concerned about "issues" around zero in divisibility questions of this type. For one thing, zero follows all of the divisibility rules followed by any other positive numbers - for example, the product of n consecutive integers is always divisible by n!, whether zero is allowed to be among those integers or not. Or as another example, "multiples of 7 are 7 apart" is still true when you include zero among your multiples of seven. So you're generally just wasting time if you consider zero as a separate case in questions like this. But there's another reason you should be especially surprised if this "exact issue shows up on test day": almost all GMAT divisibility questions are restricted to positive integers only. It's normally not even permitted for any of your numbers to be zero.
While there are many unrealistic prep company questions that test certain exceptions about zero, it is almost impossible to find any official questions that do. Prep materials that encourage test takers to spend time separating out zero as a special case in questions like the one in this thread are just using up a test taker's time during a test, time that could be spent more profitably on a different question.
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