If a and b are integers and 9

Question

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}

ENGRTOMBA2018 · Answer

How can range of possible values be just 1 value? Please check the question again.

Mascarfi · Answer

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

ENGRTOMBA2018 · Answer

Ok . It makes sense now. I was too quick to jump the gun there. 2/3 does seem logical to me.

xLUCAJx · Answer

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

TimeTraveller · Answer

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).

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