What is the product of 6 consecutive integers?


(1) The greatest integer is 4

(2) The sequence has both positive and negative integers
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From 2 statement : The sequence has both positive and negative integers
I knew the condition is Consecutive Integer, I considerd 2 cases
Case 1: Odd consecutive integer
(-3,-1,1,3,5,7) In this case the Product is Negative Integer
Case 2: Even consecutive Integers
(-4,-2,0,2,4,6) In this case product is zero
So I have chosen A

Pls help me in any analysis.

I think this is a high-quality question. This is an awesome question. I seriously faltered on the second statement. Presence of mind is important within the context what are we trying to find

1. Yes, 0! = 1 but it's highly unlikely that you'll need this for the GMAT.
2. Factorial of integer n, n!, is defined for non-negative n.
3. -1*0 = 0, and it is not the same as 0!.
4. 0*1 = 0 and it is not the same as 0!.
5. Anything*0 = 0.
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Factorial of a positive integer \(n\), denoted by \(n!\), is the product of all positive integers less than or equal to n. For instance \(5!=1*2*3*4*5\).

Note: factorial of negative numbers is undefined.
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So? What does a factorial has to do with the question at all?
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Good question.

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This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following posts:
ALL YOU NEED FOR QUANT.
Ultimate GMAT Quantitative Megathread

Hope this helps.
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You are right that:
0! == 1 >> This is true by definition

But also, the definition of factorial is:
n! = n(n-1)(n-2)...(3)(2)(1) >> It does not include 0!, also by definition

To evaluate option (2), you need to check if
- The product
- Of 6 consecutive integers
- Containing both negative and positive values
>> Gives you a unique solution

{-1, 0, 1, 2, 3, 4} is such a series:
- The product is (4)(3)(2)(1)(0)(-1) = 0
- The product can also be written as (4!)(0)(-1) = 0 >> (Anything) x 0 = 0
>> Since all series of 6 consecutive integers containing both negative and positive values MUST include 0, the product of any such series is always 0 - Unique solution
>> There is no way to re-write the product of this series with 0!

Also:
- (0)(-1) is not equal to 0!
>> 0! is defined as 1, not as n(n-1)(n-2)....
>> n! is defined as n(n-1)(n-2)...(3)(2)(1) <--- It stops at 1
>> Again, indisputably n x 0 = 0 for all n all values of n. Therefore (0)(-1) = 0, not 0! (= 1)

This is a great question! As a sidebar, under what conditions would one NOT be able to calculate the product of consecutive integers? Thank you!