Question

Let x and y be numbers such that $-y<x<y$. Which of the following must be true?
I. $|x|<y$
II. $x>0$
III. $y>0$

• A. I only
• B. I and II only
• C. I and III only
• D. I, II, and III

Answer 1

Answer: (C)

I and III only

In case I, $|x|<y$

If we open the modulus, we get $x<y$ or $x>-y$ i.e. $-y<x<y$

The valve of $y$ must be positive otherwise the value of $x$ will not exist

Therefore $y>0$

Hence, option C is correct.