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Store S sold a total of 90 copies of a certain book during

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Store S sold a total of 90 copies of a certain book during

by BTGmoderatorDC » Mon May 20, 2019 4:06 am

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Store S sold a total of 90 copies of a certain book during the seven days last week and it sold different numbers of copies on any 2 days. If for the seven days Store S sold the greatest number of copies on Saturday and the second greatest number of copies on Firday, did Store S sell more than 11 copies on Friday?

(1) Last week Store S sold 8 copies on Thursday
(2) Last week Store S sold 38 copies on Saturday

OA B

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by Ian Stewart » Mon May 20, 2019 7:08 am

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Using Statement 1 alone, Friday's sales might have been greater than 11 (from Sunday through Saturday the sales might have been 1,2,3,4,8,22,50, say) or might not have been (the sales might have been 1,2,3,4,8,10,62, say).

Using Statement 2 alone, we know that in the six days besides Saturday, 90 - 38 = 52 books were sold. So we have six different integers which add to 52, and we want to know if it is possible for the largest of those integers to be 11 or smaller. If the largest value is 11, the largest sum we could get is from this list:

6, 7, 8, 9, 10, 11

But the sum of this list (which we can compute using n*median, since the list is equally spaced) is (6)(8.5) = 51. So if the largest value in this list, which is Friday's sales, is 11 or smaller, it is impossible to sell 90 books in the week, and it must be true that at least 12 books were sold on Friday. So the answer is B.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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