If x, y, z are three positive integers such that x is greater than y and y is greater than z, then which of the following is definitely true?
(a)x% of y is greater than y% of z
(b)y% of x is greater than z% of y
(c)z% of x is greater than y% of z
(d)All of these
Answer
Answer (as printed): D
Explanation
(a) $x\% \text{ of } y=\frac{xy}{100}$ and $y\% \text{ of } z=\frac{yz}{100}$. $$x>y, y>z \Rightarrow xy>yz \Rightarrow \frac{xy}{100}>\frac{yz}{100} \Rightarrow x\% \text{ of } y>y\% \text{ of } z.$$ (b) $y\% \text{ of } x=\frac{xy}{100}$ and $z\% \text{ of } y=\frac{yz}{100}$. As proved above, $y\% \text{ of } x>z\% \text{ of } y$. (c) $z\% \text{ of } x=\frac{xz}{100}$ and $y\% \text{ of } z=\frac{yz}{100}$. $$x>y \Rightarrow xz>yz \Rightarrow \frac{xz}{100}>\frac{yz}{100} \Rightarrow z\% \text{ of } x>y\% \text{ of } z.$$ Hence all three (a), (b) and (c) hold, matching the printed answer (d) All of these.
Explanation as extracted from the printed page; notation may be imperfect.