Question

A report consisting of 2,600 words is divided into 23 paragraphs. A 2-paragraph preface is then added to the report. Is the average (arithmetic mean) number of words per paragraph for all 25 paragraphs less than 120 ?
(1) Each paragraph of the preface has more than 100 words.
(2) Each paragraph of the preface has fewer than 150 words.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is B Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

• Determining if the average number of words for $25$ paragraphs is less than $120$ is equivalent to determining if the total number of words for the $25$ paragraphs is less than $\left(25\right)\times \left(120\right)=\left(25\right)\times \left(4\right)\times \left(30\right)=\left(100\right)\times \left(30\right)=3000$. Since there are $2,600$ words in the original $23$ paragraphs, this is equivalent to determining if the total number of words in the 2 added paragraphs is less than $3000-2600=400$.
  

1. The information provided implies only that the total number of words in the 2 added paragraphs is more than $\left(2\right)\times \left(100\right)=200.$ Therefore, the number of words could be $201$, in which case the total number of added words is less than $400$, or the number of words could be $400$, in which case the number of added words is not less than $400$; NOT sufficient.
2. The information provided implies that the total number of words in the $2$ added paragraphs is less than $\left(2\right)\times \left(150\right)=300$, which in turn is less than $400$; SUFFICIENT.

• The correct answer is B; statement 2 alone is sufficient.