Let a be a positive number. If the product abc is negative, which statement must be true?
A. bc is greater than 0
B. bc uis less than 0
C. ac is greater than 0
D. ac is less than 0
E. ab is greater than 0
To determine which statement must be true when the product abc is negative, let's break it down.
We know that a is a positive number. If the product abc is negative, it means that at least one of the factors (b or c) must be negative. This is because a positive number multiplied by a negative number results in a negative number.
Now let's evaluate each statement:
A. bc is greater than 0: This statement does not necessarily have to be true. Both b and c could be negative, resulting in bc being negative.
B. bc is less than 0: This statement is true. Since at least one of the factors (b or c) must be negative, their product (bc) will always be negative.
C. ac is greater than 0: This statement does not have to be true. If b is negative and c is positive, then ac would be negative.
D. ac is less than 0: This statement does not have to be true. If b is negative and c is positive, then ac would be negative.
E. ab is greater than 0: This statement is true. Both a and b are positive, so their product (ab) will always be positive.
Therefore, the correct statement is B. bc is less than 0.