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

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a is an integer greater than 19 but less than 31, b is an integer grea  [#permalink]

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New post 12 Jul 2016, 19:04
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A
B
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E

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Question Stats:

69% (01:35) correct 31% (01:28) wrong based on 88 sessions

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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

*An answer will be posted in 2 days

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Re: a is an integer greater than 19 but less than 31, b is an integer grea  [#permalink]

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New post 12 Jul 2016, 23:32
min value of a/b will be when b is highest and a is lowest ---> a=20 and b=40
So, a/b = 1/2

max value of a/b will be when b is lowest and a is highest ---> a=30 and b=30
So, a/b = 1

Range is 1-(1/2) = 1/2.

Answer should be B.

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Re: a is an integer greater than 19 but less than 31, b is an integer grea  [#permalink]

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New post 12 Jul 2016, 23:34
the lowest value a can take = 20 = min(a)
the highest = 30 = max(a)

lowest b can take = 30 = min(b)
highest = 40 = max(b)

lowest value of a/b= min(a)/max(b) = 20/40=1/2
highest value of a/b=max(a)/min(b)=30/30=1
range = highest-lowest=1/2
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Re: a is an integer greater than 19 but less than 31, b is an integer grea  [#permalink]

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New post 13 Jul 2016, 02:40
MathRevolution wrote:
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

*An answer will be posted in 2 days

Range 1) with lowest denominator @ b=30
Numerator a Varies
from a=30 => 20/30=> 0.66
to a = 30 => 30/30 => 1

Range 2) with denominator @ b=40
Numerator a Varies
from a=20 => 20/40 =>0.5
to a = 30 =>30/40 => 0.75

The lowest and the highest possibilities of a/b is 1 - \(\frac{1}{2}\) = \(\frac{1}{2}\)
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Re: a is an integer greater than 19 but less than 31, b is an integer grea  [#permalink]

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New post 13 Jul 2016, 05:10
MathRevolution wrote:
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

*An answer will be posted in 2 days


31>a>19
41>b>29

Range= Maximum value- minimum value

Maximum value of a/b is when a is Max and b is min= 30/30= 1

Minimum value of a/b is when a is min and b is max= 20/40= 1/2

Range= 1-1/2= 1/2

B is the answer
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Re: a is an integer greater than 19 but less than 31, b is an integer grea  [#permalink]

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New post 14 Jul 2016, 21:14
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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Re: a is an integer greater than 19 but less than 31, b is an integer grea  [#permalink]

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Re: a is an integer greater than 19 but less than 31, b is an integer grea   [#permalink] 21 Feb 2018, 08:07
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