Myra multiplies 5 integers. The product is negative. AT MOST, how many of the integers could be negative?
A) 1 ***
B) 3
C) 4
D) 5
To solve this problem, we need to consider the properties of multiplying integers.
When multiplying integers, we follow these rules:
- If we multiply two positive integers, the product is positive.
- If we multiply two negative integers, the product is positive.
- If we multiply a positive integer and a negative integer, the product is negative.
Given that the product of the 5 integers is negative, we can determine the maximum number of negative integers by looking at the possible combinations of positive and negative integers.
Let's consider the scenario where all 5 integers are negative. In this case, the product would be negative since we are multiplying 5 negative integers together. Therefore, the answer is NOT D) 5.
Now, let's consider the scenario where 4 integers are negative and 1 integer is positive. In this case, the product would also be negative since we are multiplying 4 negative integers and 1 positive integer together. Therefore, the answer is POSSIBLY C) 4.
Next, let's consider the scenario where 3 integers are negative and 2 integers are positive. In this case, the product would be positive since we have an even number of negative integers. Therefore, the answer is NOT B) 3.
Finally, let's consider the scenario where 2 integers are negative and 3 integers are positive. In this case, the product would also be positive since we have an even number of negative integers. Therefore, the answer is NOT A) 1.
Based on our analysis, the maximum number of integers that could be negative, given that the product is negative, is 4. So, the correct answer is C) 4.