Question

David is thinking of two numbers, x and y. He says that if he adds them together, the sum is negative. Select all the correct explanations of how this is possible. A. Both numbers are negative. B. x is negative, and |x| > |y|. C. x is negative, and |x| < |y|. D. y is negative, and |x| < |y|. E. David is wrong. The sum of two numbers cannot be negative.

Answer 1

Answer: A, B and D.

Explanation:

We have two numbers, x and y.

And we know that:

x + y is a negative number.

Then it can happen if:

1) x and y are negative numbers.

remember that when we add two negative numbers, for example -2 and -3 we have:

-2 + (-3) = -5

The sum of two negative numbers is always negative.

2) we have a positive and a negative number, but the absolute value of the negative number is larger than the absolute value of the positive.

For example, if we have -5 and 3.

The positive number is 3 and the negative is -5

and I-5I > I3I

Then when we add those:

-5 + 3 = -2

The result is also a negative number.

Then the correct options are:

A. Both numbers are negative.

B. x is negative, and |x| > |y|. (here says that the negative number is larger in absolute value than the other)

D. y is negative, and |x| < |y|. (this is similar as above, but in this case the negative number is y)