If x is positive and y is negative, which of the following must be

Question

If x is positive and y is negative, which of the following must be true?

A. The product of x and y is positive 
B. The sum of x and y is positive 
C. The sum of x and y is negative 
D. The difference of x and y is positive 
E. The sum of x^2 and y^2 is positive

OptimusPrepJanielle · Answer

To solve this question, we need to remember the following things:
-ve * -ve = +ve
+ve *+ve = +ve
-ve * +ve = -ve

Given that x = +ve and y = -ve

Checking the options: 
A. The product of x and y is positive. FALSE
B. The sum of x and y is positive.
Cannot be said. This will depend on the values of x and y 
C. The sum of x and y is negative
This will depend on the values of x and y 
D. The difference of x and y is positive
This will depend on the values of x and y 
E. The sum of x^2 and y^2 is positive
This will always be true as the square of any number is always +ve
And the summation of 2 positive numbers will always be positive.
Correct Option: E

BrentGMATPrepNow · Answer

NOTE: this is one of those questions that require us to check/test each answer choice. In these situations,  always check the answer choices from E to A , because the correct answer is typically closer to the bottom than to the top.

E. The sum of x² and y² is positive
If x is positive and y is negative, then neither value can equal zero, which means x² and y² are each POSITIVE, which means their sum must be positive

Answer: E

IanStewart · Answer

This question has two correct answers. E is clearly correct: we're adding two nonzero squares, so we get a positive result. But D is also correct. If x is positive and y is negative, x-y is clearly positive.

There's only one imaginable justification for saying D is wrong here: someone might claim "the difference of x and y" can mean y - x (which is negative). But it can't mean that. If someone says "the difference of x and y", that can sometimes be ambiguous: they either mean "x-y", or they mean the *positive difference* of x and y, so |x - y|. But in this question, there's no ambiguity: those are the same thing. The phrase can't mean "y - x", and if someone thought it could, it clearly wouldn't make sense to talk, as answer D does, about *the* difference of x and y, if that difference can have two different values.

So there's something wrong with the question.

If x is positive and y is negative, which of the following must be

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