A report consisting of 2,600 words is divided into 23

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by AAPL » Fri Jul 27, 2018 6:59 am

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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 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.

The OA is B.

If the average is 120 words per paragraph, then for 25 paragraphs, there will be a total of 25*120 = 3000 words. So any total less than 3000 words will give an average less than 120.

(1) Each paragraph of the preface has more than 100 words.
The total number of words may or may not exceed 3000. Insufficient

(2) Each paragraph of the preface has fewer than 150 words.
The total number of words cannot exceed 2750 so the average is less than 120. SUFFICIENT

Hence, the correct answer is B.

Has anyone another approach to solving this DS question? Regards!

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Source: Beat The GMAT — Data Sufficiency | Fri Jul 27, 2018 6:59 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Fri Aug 31, 2018 11:21 am

Here, Determine if the average number of words for 25 paragraphs is less than 120 is the same as finding the total number of words for the 25 paragraphs which is less than 120*25=3000

Since there are 2600 words in the original 23 paragraph. This is equivalent to finding the total number of words in the 2 added paragraphs in the preface which will be less than 3000-2600= less than 400.

Statement 1= Each paragraph of the preface has more than 100 words.
This means that the 2 new paragraph of the preface is greater than 100*2 = greater than 200. thus, there is a possibility of the 2 new paragraphs to be greater than 400 in the preface. The entire word count will be greater than 3000 and the average number of words will be greater than 120. Hence, statement is INSUFFICIENT

Statement 2= Each paragraph of the preface has fewer than 150 words.
This means that the 2 new paragraphs in the preface is less than 150*2 = less than 300. Thus, it is less than 400 which in turn makes the total word count less than 300 and the average number of words less than 120. Hence, statement 2 is SUFFICIENT

Therefore, the final answer is option B

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