If a is an integer greater than 4 but less than 21 and b is an integer

Question

If a is an integer greater than 4 but less than 21 and b is an integer greater than 14 but less than 31, what is the range of a/b?

A. 2/3
B. 1/2
 C. 5/6 
D. 1 
E. 7/6

Rushilkhera · Accepted Answer

The way to approach this problem is 4<a<21 and 14<b<31

Minimum possible value of a is 5 and maximum is 20
Minimum possible value of b is 15 and maximum is 30

Range = max a/min b - min a/max b
(Highest - lowest)

20/15 - 5/30 = 7/6

Hence E

0akshay0 · Answer

The range of a/b = max(a/b) - min(a/b) a/b will be max when we select max value for a and min value for b from given range a/b will be minwhen we select max value for b and min value for a from given range range of a/b = max(a/b) - min(a/b) = 20/15 - 5/30 = 4/3 - 1/6 = 7/6 Hence option E is correct Hit Kudos if you liked it 8-)

ScottTargetTestPrep · Answer

A positive fraction is maximized when the numerator is as large as possible and the denominator is as small as possible. Thus, the maximum value of a/b is 20/15 = 4/3.

Similarly, a positive fraction is minimized when the numerator is as small as possible and the denominator is as large as possible; thus, the minimum value of a/b is 5/30 = 1/6.

Therefore, the range of values of a/b is 4/3 - 1/6 = 8/6 - 1/6 = 7/6.

Answer: E

CrackverbalGMAT · Answer

Given that the integers a and b have the following values

4 < a < 21: a can take the values 5,6,7,8.. till 20

14 < b < 31: b can take the values 15,16,17.. till 30

We take all the possible value of a/b and then see which is the smallest and the largest

a = 5, b = 15: a/b = 1/3 = 0.333

a = 5, b = 30: a/b = 1/6 = 0.167

a = 20, b = 15: a/b = 20/15 = 1.333

a = 20, b = 30: a/b = 20/30 = 0.667

Smallest Value = 1/6 and the Largest Value = 4/3

Therefore Range = Largest Value - Smallest Value = 4/3 - 1/6 = 7/6

Option E

Arun Kumar

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If a is an integer greater than 4 but less than 21 and b is an integer

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If a is an integer greater than 4 but less than 21 and b is an integer

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