Guide 5, Chapter 2, Pg. 40

[Jmoustafa345]

My thought process for question #6 was, since there are 1/4 more consonants than variables, I set up the number of consonants to be V+1/4V, or 5/4V. To find the total number of letters, the equation I set up was V+5/4V, or 9/4V. I'm getting the wrong answer (actually, two answers end up working), I'm just not sure where I'm going wrong.

[tommywallach]

Hey J,

No, your solution is fine, but remember, the questions asks "which of the following is a possibility..." Whenever you see this word, it's telling you the question won't "solve". Solving would mean ONE answer. If we're only finding a POSSIBLE answer, we aren't solving...we're inferring from a set of rules.

Your equation is correct:

Letters = 9/4v

And because we need the number of letters, the number of vowels, and the number of consonants to be integers, we can plug in all the answer choices. Only B gets us an integer for all of these.

(You noticed that 12 also gets you an integer for the number of letters, but it won't get you integers for both the consonants and vowels individually. Which is why this method is a rough one...it takes forever to work out!).

-t