M7MBA wrote:If a and b are integers and 9 < a < 21 and 19 < b < 31, what is the range of the possible values for a/b?
A) 12/19
B) 120/589
C) 12/31
D) 2/3
E) 480/589
Since a must be an integer:
10 ≤ a ≤ 20.
Since b must be an integer:
20 ≤ b ≤ 30.
Greatest option for a/b:
(greatest possible a)/(smallest possible b) = 20/20 = 1.
Smallest option for a/b:
(smallest possible a)/(greatest possible b) = 10/30 = 1/3.
Range:
(greatest a/b) - (smallest a/b) = 1 - 1/3 = 2/3.
The correct answer is
D.
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