jainrahul1985 wrote:If M is a finite set of negative integers, is the total number of integers in M an odd number?
(1) the product of all integers in M is odd
(2) product of all integers is negative
We are given that M is a finite set of negative integers and we need to determine whether the total number of integers in M is an odd number.
Statement One Alone:
The product of all the integers in M is odd.
The information in statement one is not sufficient to answer the question. For instance, there could be 2 numbers in M, -1 and -3, and their product would be odd, or there could be 3 numbers in M, -1, -3, and -5, and their product would also be odd. Statement one alone is not enough information to answer the question.
Statement Two Alone:
The product of all the integers in M is negative.
To analyze the information provided in statement two, we can use our multiplication rules for negative numbers. We know that when an even number of negative numbers are multiplied together, the product is positive, and when an odd number of negative numbers are multiplied together, the product is negative.
Since the product of all the integers in M is negative, we know that the number of integers in M must be odd.
Answer:
B
