If 0<r<1<s<2, which of the following

[gphil]

One more question. Thanks for help!!!

If 0<r<1<s<2, which of the following must be less than 1?

I. r/s
II. r*s
III. s - r

A) I only - correct answer
B) II only
C) III only
D) I and II
E) I and III

I don't understand why A is the correct? I picked different numbers and it looks like D) I and II correct. ???

[Amit]

If 0<r<1<s<2, which of the following must be less than 1?

I guess the only situation you're missing is a case where r*s is incorrect. Make sure you always try the extremes of each number.

Try s=1.9 and r=0.9.

s*r = approx 1.7 which is > 1.

[gphil]

Thanks a lot, Amit. It was helpful!

[NNK314]

Curious if this can be solved this way:

Given: 0<r<1<s<2

1. r/s <1
= r<s (yes)

2. rs<1
= r<1/s (no)

3. s-r<1
= s<r (no)

So only 1 must be true?

One more question. Thanks for help!!!

If 0<r<1<s<2, which of the following must be less than 1?

I. r/s
II. r*s
III. s - r

A) I only - correct answer
B) II only
C) III only
D) I and II
E) I and III

I don't understand why A is the correct? I picked different numbers and it looks like D) I and II correct. ???

[RonPurewal]

1. r/s <1
= r<s (yes)

^^ this makes sense.

2. rs<1
= r<1/s (no)

^^ this is a valid algebraic transformation, but I'm not sure how you could just look at 0 < r < 1 < s < 2 and just see that r < 1/s is false.

3. s-r<1
= s<r (no)

^^ this is not valid (what happened to the "1"?)