2012-02-23 09:00:02

A sequence of 4 consecutive integers is multiplied together. Which of the following could be their product?

I. -24
II. 0
III. 24

A) I only
B) II only
C) III only
D) II and III only
E) I, II, and III only

The correct answer is D

Explanation: Since the question asks what "could be true," if you can find one situation in which the statement in question works, then it is a correct answer. Check each statement individually, and cross off any answer choice that contains a Roman Numeral that does not work or does not contain one that does work. Let's start with III, since it appears in most of the answer choices.

III: This works for the lowest four positive numbers: 1, 2, 3, 4. 4! (4 factorial) is 24, as 4 x 3 x 2 x 1 = 24.  Get rid of answer choices A and B since they do not contain Statement III, which is clearly true. Now, check statement II.

II: This works, as any set of numbers multiplied by 0 will always be 0. Thus, -3, -2, -1, and 0 will have a product of 0, as will any other set of consecutive integers hovering around 0. Cross out answer choice C since it does not include statement II. Finally, check statement I.

I: This will not work for any numbers, since the product of an even set of numbers would only be negative if there were an odd number of negative numbers. However, any number set that contains both odd and even numbers, in this case, would have to include 0, since the number sets here are all consecutive numbers (so, if  a set contained -1, 1, and 2, it would also include 0). Anything multiplied by 0, of course, will have a product of 0, not -24. Thus, cross out choice E. This leaves one answer, the correct one: choice D.