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

Ans. B

Use spoiler for OA.

St1 : { -3, -5} product of the both gives a odd number. But he number of elements in the set is even
{-1,-3,-5} product of the both gives a odd number.But he number of elements in the set is odd

So st 1 leads to inconsistency. Insufficient.

St 2: product of all integers is negative

This can happen only when the set is having odd number of elements. Consistent . So sufficient.YES
ex: {-1,-2,-3}=-6(negative number)

Pick B

Basically in Number systems what i understood is however we are good in fundae, on the given test day "picking numbers" will do the trick.

Statment 1 deals with the issue of even/odd - which has set rules for addition, multiplication and subtraction. if the product of all the integers is odd that means that there are no even numbers in the set - but doesn't give us any info as to how many numbers there are.

Stmt 2 deals with the rules of neg/pos - if you have a set of negative numbers whose product is negative then there has to be an odd number as an even number of negatives multiplied together will always give you a postive number.

So B.

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