Total Test Questions

Date: 09/21/97 at 04:10:57
From: Patrick
Subject: SAT question

On her biology test, Cathy answered 5/6 of the questions correctly.  
If Cathy answered 18 of the first 27 questions correctly, then the 
total number of questions on the test must be at least:

(A) 32  (B) 36  (C) 45  (D) 48  (E) 54

Date: 09/21/97 at 13:31:11
From: Doctor Sonya
Subject: Re: SAT question

Dear Patrick,

This is a hard question!  I think the SATs must have been easier when 
I took them.

Okay, let's figure out how to solve this problem. It's a word problem, 
and the first thing you always do with word problems is figure out 
what information you have. We know what proportion of the test Kathy 
got right. We also know that of the first 27, she got 18 right. This 
also means that she got 9 wrong.  Do you see how I got that? 

The problem asks for the least possible number of questions on the 
test. I want to assume that she answers all of the rest of the 
questions right, because this gives us the _least_ number of 
questions. If she answers some of the rest of them incorrectly, she 
will have to answer even more of them correctly to make up for it, and 
we won't have the least possible number any more.

If Kathy answers 5/6 of the questions correctly, she must answer 1/6 
of them incorrectly. We already figured out that the number she 
answers incorrectly is 9, so 9 is 1/6 of the total number of questions 
on the test. Let's call this number q.  

If we write this in equation form, we get:  (1/6)q = 9.
Then you just have to solve this equation for q to get the answer.

I hope this helps.  Feel free to write us back if you have any more 
questions.

-Doctor Sonya,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/