q: 85 white and black tiles will be used to form a 10x10 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?
Options:
(A) 75
(B) 80
(C) 85
(D) 90
(E) 95
a: Answer = A
Please refer diagram below
85 - 10 = 75 The answer is (A).
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q: Last year, Company M made q dollars in profit. Half of the profit went to the company’s founder. The rest was split evenly among his Three other partners. In terms of q, how much did each of the other partners receive?
Options:
(A) q/4
(B) q/5
(C) q/6
(D) q/7
(E) q/8
a: Profit = q
Profit to company founder = q/2
Profit to other partners = q/2
Number of other partners = 3
Profit to each partner = (q/2)/3 = q/6 The answer is (C).
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q: A pharmaceutical company received $4 million in royalties on the first $50 million in sales of and then $12 million in royalties on the next $170 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $50 million in sales to the next $170 million in sales?
Options:
(A) 12%
(B) 15%
(C) 45%
(D) 52%
(E) 56%
a: (12/170)/(4/50) = 15/17 = 88% it means that 12/170 represents only 88%. Therefore a decrease of 12%. The answer is (A).
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q: John's grade was 80th percentile of the 100 grades for his class. Of the 60 grades from another class, 20 were higher than John's, and the rest were lower. If no other grade was the same as John's grade, then John's grade was what percentile of the grades of the two classes of two classes combined?
Options:
(A) 72nd
(B) 75th
(C) 83rd
(D) 85th
(E) 94th
a:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
72nd/75th/83rd/85th/94th The answer is (B).
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