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### 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/
```
Associated Topics:
Middle School Algebra
Middle School Word Problems

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