If Wayne considers the letter "Y" to be a vowel but Kristen does not, thinking that there are only 5 vowels, by what percent is the probability that a randomly selected letter out of the 26 letter alphabet will be a vowel greater in Wayne's opinion than in Kristen's opinion? A)$5$% ; B) $6$% ; C) $20$% ; D) $30$% ; E) $32$%
So for Wayne, the probability of a randomly selected letter being a vowel is $\frac{6}{26}$. For Kristen, it is $\frac{5}{26}$. Then clearly, the difference is $1/26$, and so I thought the percentage would be $\frac{1}{26} \cdot 100 = 3.85$%, but that's none of the answer choices. Rather, the solution says that I should do $\frac{1/26}{5/26} = 20$%, but I don't understand why $5/26$ should be in the denominator.
The question statement is phrased somewhat confusingly. Here's a better way to put things :
In other words, by what percentage is "$a$" greater than "$b$"? (Where $a$ and $b$ are something that you need to calculate).
To solve such a question, you find what $a$ and $b$ are, then find out by how much $a$ exceeds $b$, and the ratio between this difference and $b$ is what you are seeking. For example : "by what percentage does $35$ exceed $25$"? Your answer would be $\frac {35 - 25}{25} = \frac 25 = 40%$.
In a similar manner, for the question given to you, we have $a = \frac 6{26}$ and $b = \frac 5{26}$. Now you see why the answer is $\frac 15 = 20%$.
The rephrasing of the question, and therefore understanding it, is sometimes more crucial than the question itself. Next time, you should read questions like this more carefully.