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a is an integer greater than 19 but less than 31, b is an in

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by Max@Math Revolution » Tue Jul 12, 2016 6:04 pm
a is an integer greater than 19 but less than 31, b is an integer greater than 29 but less than 41, what is the range of a/b?
A. 1/4
B. 1/2
C. 3/4
D. 1
E. 5/4

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by Brent@GMATPrepNow » Wed Jul 13, 2016 10:03 am
Range of a/b = (maximum value of a/b) - (minimum value of a/b)

maximum value of a/b
This occurs when a is as large as possible and when b is as small as possible
Max value of a = 30
Min value of b = 30
So, maximum value of a/b = 1

minimum value of a/b
This occurs when a is as small as possible and when b is as large as possible
Min value of a = 20
Max value of b = 40
So, minimum value of a/b = 1/2

----------------------------
Range of a/b = (maximum value of a/b) - (minimum value of a/b)
= (1) - (1/2)
= [spoiler]1/2[/spoiler]
= B
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by Max@Math Revolution » Mon Jul 18, 2016 3:08 am
From 20≤a≤30 and 30≤b≤40, we get 1/2=20/40≤a/b≤30/30=1. Hence, range=Max-min=1-1/2=1/2 and the correct answer is B.
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by Max@Math Revolution » Mon Jul 18, 2016 3:09 am
From 20≤a≤30 and 30≤b≤40, we get 1/2=20/40≤a/b≤30/30=1. Hence, range=Max-min=1-1/2=1/2 and the correct answer is B.
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