lheiannie07 wrote:Pat is reading a book that has a total of 15 chapters. Has Pat read at least 1/3 of the pages in the book?
(1) Pat has just finished reading the first 5 chapters.
(2) Each of the first 3 chapters has more pages than each of the other 12 chapters in the book.
Test EXTREMES.
Statements combined:
Case 1: The first 3 chapters have 11 pages each, the next 2 chapters have 1 page each, and the last 10 chapters have 10 pages each.
In this case:
Pages in the first 5 chapters = (pages in the first three 11-page chapters) + (pages in the next two 1-page chapters) = (3*11) + (2*1) = 35.
Total number of pages = (pages in the first five chapters) + (pages in the last ten 10-page chapters) = 35 + (10*10) = 135.
Fraction read by Pat = 35/135 = 7/27.
Since 9/27 = 1/3, the fraction read by Pat is LESS than 1/3.
Thus, the answer to the question stem is NO.
Case 2: The first 3 chapters have 100 pages each, and the last 12 chapters have 1 page each.
In this case:
Pages in the first 5 chapters = (pages in the first three 100-page chapters) + (pages in the next two 1-page chapters) = (3*100) + (2*1) = 302.
Total number of pages = (pages in the first five chapters) + (pages in the last ten 1-page chapters) = 302 + (10*1) = 312.
Fraction read by Pat = 302/312 = MORE than 1/3.
Thus, the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.
The correct answer is
E.
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