Positives and Negatives

[tonebeeze]

A certain list consists of several different integers. Is the product of all the integers in the list positive?

1. The product of the greatest and smallest of the integers in the list is positive.

2. There is an even number of integers in the list.

OA = C

[djiddish98]

To solve, we need to know how many negative integers we have. If we had an odd amount, then we'll have a negative product. If it's even, then we'll have a positive product.

Statement 1: This tells us that either all of the integers are positive or all of the integers are negative. If the product of the largest and smallest is positive, that means the largest and smallest are both negative (and therefore all numbers in between) or largest and smallest are both positive (and all numbers in between).

All numbers can be negative in this instance, and we're still not sure if we have an even number of negatives or odd. Hence, this is insufficient

Statement 2: Even if the total number of integers is even, we're still not sure if we have an odd number of negative numbers. We could have a set like {-1, 1,2,3,4,5} which would be negative despite have 6 integers.

Combined: Statement 1 tells us all integers are either negative or positive. We also know that there are an even number of those integers. An even number of all negative integers would lead to a positive, so we know our answer.

[Brent@GMATPrepNow]

A certain list consists of several different integers. Is the product of all the integers in the list positive?

1. The product of the greatest and smallest of the integers in the list is positive.

2. There is an even number of integers in the list.

OA = C

Statement 1:
case a: {-3, -1} product is positive
case b: {-3, -2, -1} product is negative
INSUFFICIENT

Statement 2:
case a: {-3, -1} product is positive
case b: {-3, 1} product is negative
INSUFFICIENT


Statements 1 AND 2:
Statement 1 tells us that the smallest and largest integers are either both positive or both negative
This means that the integers in the set are either ALL positive or ALL negative

Case a: the integers in the set are ALL positive
This means the product must be positive

Case b: the integers in the set are ALL negative
Since there is an even number of integers, we can pair up every negative integer with another.
Since the product of each pair will be positive, the entire product must be positive

In both cases, the product must be positive --> SUFFICIENT C

Cheers,
Brent

[ankurmit]

--