## A report consisting of 2,600 words…

## Solution:

We are given that a report consisting of 2,600 words is divided into 23 paragraphs. We are also given that that report has an added 2-paragraph preface. We must determine whether the average number of words per paragraph is less than 120 words. If we let x = the number of words in paragraph one of the preface and y = the number of words in paragraph two of the preface we can insert all of our information into the average formula, which is

average = sum/number

Is the average number of words per paragraph < 120 words?

Is (2,600 + x + y)/25 < 120?

Is 2,600 + x + y < 3,000?

Is x + y < 400?

We need to determine whether the total number of words in the two paragraphs of the preface is less than 400 words.

**Statement One Alone: **

Each paragraph of the preface has more than 100 words.

Using the information in statement one, we do not have enough information to determine whether x + y is less than 400. We could have a case in which the number of words in the preface is 300 words, or we could have a case in which the number of words in the preface is 500 words. We can eliminate answer choices A and D.

**Statement Two Alone: **

Each paragraph of the preface has fewer than 150 words.

Using the information in statement two we see that, at most, each paragraph in the preface has 149 words, which would give a total of 298 words for the entire preface. Thus, we know that x + y is less than 400. Statement two alone is sufficient to answer the question.

**Answer: B **