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If a and b are integers and 9 < a < 21 and 19 < b < 31, what is the ra

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If a and b are integers and 9 < a < 21 and 19 < b < 31, what is the ra  [#permalink]

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New post 20 Jul 2015, 13:41
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If a and b are integers and 9 < a < 21 and 19 < b < 31, what is the range of the possible values for \(\frac{a}{b}\)?

A) \(\frac{12}{19}\)
B) \(\frac{120}{589}\)
C) \(\frac{12}{31}\)
D) \(\frac{2}{3}\)
E) \(\frac{480}{589}\)
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Re: If a and b are integers and 9 < a < 21 and 19 < b < 31, what is the ra  [#permalink]

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New post 20 Jul 2015, 14:13
Mascarfi wrote:
If a and b are integers and 9 < a < 21 and 19 < b < 31, what is the range of the possible values for \(\frac{a}{b}\)?

A) \(\frac{12}{19}\)
B) \(\frac{120}{589}\)
C) \(\frac{12}{31}\)
D) \(\frac{2}{3}\)
E) \(\frac{480}{589}\)


How can range of possible values be just 1 value? Please check the question again.
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Re: If a and b are integers and 9 < a < 21 and 19 < b < 31, what is the ra  [#permalink]

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New post 20 Jul 2015, 14:29
I thaught the same, thats why i put it here. A trap i have not yet found...

You have that they are integers, so the biggest possible value for a/b is the biggest value of a divided by the smallest value of b...20/20 = 1

...the smallest possible value for a/b is the smallest value of a divided by the biggest value of b...10/30= 1/3...

Then you have:

1 - (1/3) = 2/3
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Re: If a and b are integers and 9 < a < 21 and 19 < b < 31, what is the ra  [#permalink]

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New post 20 Jul 2015, 14:36
Mascarfi wrote:
I thaught the same, thats why i put it here. A trap i have not yet found...

You have that they are integers, so the biggest possible value for a/b is the biggest value of a divided by the smallest value of b...20/20 = 1

...the smallest possible value for a/b is the smallest value of a divided by the biggest value of b...10/30= 1/3...

Then you have:

1 - (1/3) = 2/3


Ok . It makes sense now. I was too quick to jump the gun there. 2/3 does seem logical to me.
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Re: If a and b are integers and 9 < a < 21 and 19 < b < 31, what is the ra  [#permalink]

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New post 20 Jul 2015, 15:22
1
Range: Largest-Smallest

The largest number would have largest A value and smallest B value

A=20 B=20

20/20=1

Smallest value: smallest A value and largest B value
A=10 B= 30

1-(10/30)

30-10/30=20/30=2/3
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Re: If a and b are integers and 9 < a < 21 and 19 < b < 31, what is the ra  [#permalink]

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New post 21 Jul 2015, 08:47
\(Range = Maximum(\frac{a}{b}) - Minimum(\frac{a}{b})\)

\(Maximum(\frac{a}{b})\) is when \(a\) is maximum and \(b\) is minimum = \(\frac{20}{20} = 1\).

\(Minimum(\frac{a}{b})\) is when \(a\) is minimum and \(b\) is maximum = \(\frac{10}{30} = \frac{1}{3}\).

Range = \(1 - \frac{1}{3} = \frac{2}{3}\). Ans (D).
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Re: If a and b are integers and 9 < a < 21 and 19 < b < 31, what is the ra   [#permalink] 21 Jul 2015, 08:47
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