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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If a and b are integers and 9 < a < 21 and 19 < b < 31, what is the ra post reply Question banks Downloads My Bookmarks Reviews Important topics
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Manager  Joined: 08 May 2015
Posts: 86
GMAT 1: 630 Q39 V38 GMAT 2: 670 Q44 V38 GMAT 3: 750 Q49 V44 If a and b are integers and 9 < a < 21 and 19 < b < 31, what is the ra  [#permalink]

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1 00:00

Difficulty:   35% (medium)

Question Stats: 60% (00:59) correct 40% (02:15) wrong based on 11 sessions

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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) $$\frac{480}{589}$$
CEO  S
Joined: 20 Mar 2014
Posts: 2560
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If a and b are integers and 9 < a < 21 and 19 < b < 31, what is the ra  [#permalink]

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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.
Manager  Joined: 08 May 2015
Posts: 86
GMAT 1: 630 Q39 V38 GMAT 2: 670 Q44 V38 GMAT 3: 750 Q49 V44 Re: If a and b are integers and 9 < a < 21 and 19 < b < 31, what is the ra  [#permalink]

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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
CEO  S
Joined: 20 Mar 2014
Posts: 2560
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If a and b are integers and 9 < a < 21 and 19 < b < 31, what is the ra  [#permalink]

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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.
Current Student Joined: 22 Apr 2015
Posts: 44
Location: United States
GMAT 1: 620 Q46 V27 GPA: 3.86
Re: If a and b are integers and 9 < a < 21 and 19 < b < 31, what is the ra  [#permalink]

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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
Senior Manager  B
Joined: 28 Jun 2015
Posts: 279
Concentration: Finance
GPA: 3.5
Re: If a and b are integers and 9 < a < 21 and 19 < b < 31, what is the ra  [#permalink]

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$$Range = Maximum(\frac{a}{b}) - Minimum(\frac{a}{b})$$

$$Maximum(\frac{a}{b})$$ 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).
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that. 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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