inequalities

[earth@work]

If r > t and r < 1 and rt = 1, then which one of the following must be 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

Ans : B

[cramya]

r>t i.e. t<r 1)

r<1 2)

Add inequalities facing same direction

r+t < r+1

Add -r to both sides

t<1

We have:

r<1
t<1
r>t
rt=1

r>-1 and t<-1 is the one that must be true (I picked numbers)

r=-1/5 t=-5 rt=1

Hoping I dint miss something here!
B)

[Ossa]

Hi,
If you look at the different options you can quickly eliminate some of them:

A) r > 0 and t < –1, if t<-1, this means that t is a negative number, and so for rt to be equal to 1, then r has to be a negative number too, which contradicts with r>0, so this can not be the right answer
C) r < –1 and t > –1, this can not be true because this means that t>r, and we already know that r>t, so this option can not be the right answer
D) r < 1 and t > 1, but this means that t>r and we already know that r>t, so this can not be the right answer
E) r > 1 and t < 0, this can not be true because we know that r<1
Which leaves us with option B
B) r>-1, and t<-1, this would work because this does not contradict any of the facts given

I hope this helps.

If r > t and r < 1 and rt = 1, then which one of the following must be 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

Ans : B

[earth@work]

thanks Ossa & cramya for helping