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14 Jul 2006, 04:24
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Each page of a 676-page manuscript contains at least 1 and as many as four spelling mistakes. Is the average number of mistakes per page more than 2.5?
(1) The median number of mistakes is 3.5
(2) Among the pages of the manuscript, 4 is the most common number of mistakes.
(1) The median number of mistakes is 3.5
(2) Among the pages of the manuscript, 4 is the most common number of mistakes.
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I think A is the correct answer.
Since the median is 3.5 we know that 676/2 pages must contain 4 spelling mistakes and at least one page must contain 3 spelling mistakes. Since every other page must contain at least one spelling mistake, the mean must be above 2.5.
(2) is not sufficient.
For example 226 = number of pages with 4 spelling mistakes,
225 = number of pages with 2 spelling mistakes = number of pages with
1 spelling mistake => mean <2.5
226*4+225*2+225*1=904+450+225=1579 < 1600 = 640*2.5 < 676*2.5
All pages include 4 spelling mistakes => mean=4.
[In my first example. the number of pages wasn't an integer]
Since the median is 3.5 we know that 676/2 pages must contain 4 spelling mistakes and at least one page must contain 3 spelling mistakes. Since every other page must contain at least one spelling mistake, the mean must be above 2.5.
(2) is not sufficient.
For example 226 = number of pages with 4 spelling mistakes,
225 = number of pages with 2 spelling mistakes = number of pages with
1 spelling mistake => mean <2.5
226*4+225*2+225*1=904+450+225=1579 < 1600 = 640*2.5 < 676*2.5
All pages include 4 spelling mistakes => mean=4.
[In my first example. the number of pages wasn't an integer]
14 Jul 2006, 07:21
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good trap.
D.
1. we should not forget that there are 338(676/2) fours (4's) and at least one 3 (three). the avg becomes >2.5.
2. there are more than 169 fours (4's) and none can be more than 169. so also suff. the avg is > (1+2+3+4)/4.
D.
1. we should not forget that there are 338(676/2) fours (4's) and at least one 3 (three). the avg becomes >2.5.
2. there are more than 169 fours (4's) and none can be more than 169. so also suff. the avg is > (1+2+3+4)/4.
