1. ## data sufficiency question

you have to select if the 1st piece of information will answer the question alone, if the second will answer the question alone. or if you need both pieces to answer the question. here is the problem:

a cetain list contains several different integers. is the product of all the integers positive?

1. the product of the greatest integer and the smallest is positive

2. the list contains an even number of integers.

the answer is both of the pieces of information are needed to answer the question. i thought that each piece of information by itself would be sufficient. does anyone know why you would need both pieces to answer the question? thanks

2. Originally Posted by helpjoe
you have to select if the 1st piece of information will answer the question alone, if the second will answer the question alone. or if you need both pieces to answer the question. here is the problem:

a cetain list contains several different integers. is the product of all the integers positive?

1. the product of the greatest integer and the smallest is positive

2. the list contains an even number of integers.

the answer is both of the pieces of information are needed to answer the question. i thought that each piece of information by itself would be sufficient. does anyone know why you would need both pieces to answer the question? thanks
Neither is sufficient to answer the question by itself.

To refute #1 note that the list of integers may all be negative, in which case the product of the greatest and smallest will be positive. But we are not guarenteed that the product is positive: Consider the set of integers {-4, -2, -1}. The product of these is negative.

To refute #2 note that if we have the set {-2, 1, 3, 4}, the product is negative.

So, if BOTH 1 and 2 are correct, what do we have? We have a list of purely negative integers (from 1) and we have an even number of them (from 2). What is the sign of the product of an even number of negative integers? It is positive.

-Dan

3. Originally Posted by topsquark
Neither is sufficient to answer the question by itself.

To refute #1 note that the list of integers may all be negative, in which case the product of the greatest and smallest will be positive. But we are not guarenteed that the product is positive: Consider the set of integers {-4, -2, -1}. The product of these is negative.

To refute #2 note that if we have the set {-2, 1, 3, 4}, the product is negative.

So, if BOTH 1 and 2 are correct, what do we have? We have a list of purely negative integers (from 1) and we have an even number of them (from 2). What is the sign of the product of an even number of negative integers? It is positive.

-Dan

dummy me... i was basing my answer on "even"--- thanks for pointing that out to me--- you are awesome!!!