Walkabout wrote:
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.
Target question: Is the average (arithmetic mean) number of words per paragraph for all 25 paragraphs less than 120?When it comes to averages, we know that
average value = (sum of n values)/nWe can rewrite this into a useful formula:
sum of n values = (average value)(n)So, if 25 paragraphs were to have an average EQUAL TO 120 words, then the TOTAL number of words = (120)(25) = 3000
We want to determine whether or not the average is LESS THAN 120. This will occur when the total number of words is LESS THAN 3000
So, we could rephrase the target question as follows...
REPHRASED target question: Is the total number of words less than 3000?IMPORTANT: When I
scan ahead, I see that the two statements tell us about the number of words in the PREFACE. So, let's rephrase the target question so that it pertains to the preface only.
Since the report (without the preface) contains 2600 words, the preface must have FEWER THAN 400 words in order to keep the entire word count under 3000 words. So, we can RE-REPHRASE the target question as follows:
RE-REPHRASED target question: Does the preface contain fewer than 400 words?Now that we've rewritten the target question to suit the statements, the rest of the question is a breeze.
Statement 1: Each paragraph of the preface has more than 100 words In other words, the preface contains more than 200 words. There are several possibilities. Here are two:
Case a: the preface contains 220 words, in which case
the preface contains fewer than 400 wordsCase b: the preface contains 450 words, in which case
the preface DOES NOT contain fewer than 400 wordsSince we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: Each paragraph of the preface has fewer than 150 words In other words, the preface contains fewer than 300 words.
If the preface contains FEWER than 300 words, then we can be certain that
the preface contains fewer than 400 wordsSince we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
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