inequalities topic

Question

if r>t and r<1 and rt=1 then which one of the following is true?

 

 

(a)r>0 and t<-1

(b)r>-1 and t<-1

(c)r<-1 and t<-1

(d)r<1 and t>1

(e)r>1 and t<0

Answer 1

(b) is correct.

 

Plot:

 

r=t (a horizontal line)

 

r=1 (a line passing through the origin with slope 1)

 

r=(1/t) (a hyperbola with two branches, with r>0 when t>0 and r<0 when t<0)

 

The region between the first two equations is the feasible region.  The positive hyperbola branch does not enter the feasible region.  The negative hyperbola branch passes through the feasible region and enters it at (-1,-1)