Bunuel

If x and y are letters which correspond to points on the number line shown above, which of the following statements must be true?
A. \(x > y\)
B. \(\frac{1}{x} < \frac{1}{y}\)
C. \(\frac{1}{x}*\frac{1}{y} > 9\)
D. \(xy < \frac{1}{3}\)
E. \(x+y > 1\)
coled90 I got you covered!
From the graph we know \(0 < x < \frac{1}{3}\) and \(\frac{1}{3} < y < 1\).
So first we can conclude y > x, so A is incorrect. Observe option B, since both x and y are positive we can get \(\frac{1}{x} > \frac{1}{y}\) so B is incorrect.
Options C and D focus on \(x*y\), since both x and y are positive we can take the maximum value of each piece and multiply to find the maximum of x * y. Therefore \(x*y < \frac{1}{3} * 1\) and we can choose D. (To make option C correct we should have >3 instead of >9).
Note we must confirm either x or y must be positive in order to find such a maximum for xy (since negative*negative might create a new maximum).
Ans: D