A good question to understand the technique of using simple values to solve Must be questions.
Remember that, in a Must Be true question, we take values and try to prove every option FALSE. If you proved an option FALSE, you proved that it is not always true and hence the option can be eliminated. The option remaining at the end of this process will be the correct answer.
Let’s consider x = 1 and y = -1. Using these values, let us evaluate the answer options.
x + y = 0, therefore, answer option A is false. Eliminate.
\(x^2\) – \(y^2\) = 0, therefore, answer option B is false. Eliminate.
\(y^2\) – x > 0, therefore, answer option C is false. Eliminate.
y + \(x^2\) > 0, therefore, answer option D is false. Eliminate.
This means that none of the options A, B C or D are always true.
The correct answer option is E.
A smart technique to plug values in GMAT Quant questions is to use the number line. Divide the number line into 4 standard intervals namely, 0 to 1, 1 to infinity, 0 to -1 and -1 to –infinity. Pick different types of numbers – integers, fractions, roots – from all intervals. But more importantly, do not forget to start off with ZERO, ONE and -1 because these are values that will help you answer a lot of questions.
Hope that helps!
Aravind BT