2012-07-11 09:00:31

If x and y are both negative integers, which of the following must be true?

I. xy > x
II. x/y < x
III. x - y > x

A) I only
B) II only
C) I and II
D) I and III
E) I, II, and III

The correct choice is D

Explanation:  Take this one Roman Numeral at a time.

I. is true because xy is the product of two negatives, and the product of two negatives will always be positive. Thus xy will be greater than x, since x is negative. To check this, pick two numbers for x and y. Let x be -2 and y be -3: (-2)(-3) = 6, and 6 > -2.

II. is never true. The quotient of two negatives is always positive, and a positive number will never be lower in value than a negative one. To check this, pick two numbers for x and y. Let x be -2 and y be -3: -2/-3 = 2/3, but 2/3 is not less than -2.

III. is always true. When two negatives are subtracted from each other, the result is a larger number (either a negative number closer to 0 or a positive number). To check this, pick two numbers for x and y. Let x be -2 and y be -3: (-2) - (-3) = 1, and 1 > -2. This holds true with different numbers too. Let x be -10 and y be -4: (-10) - (-4) = -6, and -6 > -10.

Since I and III work, choice D is correct.