Problem Solving

Hey guys, here is another one !

0 < r < 1 < s < 2

Which of the following must be < 1 ?

I) r/s
II) rs
III)s-r


A) I only
B) II only
C) III only
D) I & II
E) I & III



r = 1/2 s = 3/2

I) r/s = (1/2)/(3/2) = (1/2) * (2/3) = 1/3 --> true
II) rs = (1/2)*(3/2) = 3/4 --> true
III) s-r = 3/2 - 1/2 = 2 --> false

Other numerical test:
r = 1/100 s = 199 / 100

I)r/s = (1/100) / (199/100) = 1/199 ---> true
II) rs = (1/100) * (199/100) = 199/1000 --> true
III) s-r = (199/100)-(1/100) = 198/100 --> false

IMO : D

OA : A

I think instead of picking numbers here, you should actively think of ways to contradict each of the three statements. Even if you pick 2 sets of numbers, that doesn't necessarily cover all your bases. It's not a bad strategy, but there's a chance you miss something.

Instead, I'd suggest thinking about how extremes alter each of the three, and try to find a pair of r,s that doesn't make it <1.

I think that any number multiplied by r, with r being between 0 and 1 will be < 1, no ?

Can you find that set of number for which sr > 1 ?

I'm getting crazy over it :twisted:

r= 3/4
s= 5/3

rs= 3/4*5/3=5/3>1

r= 3/4
s= 5/3

rs= 3/4*5/3=5/4>1

Sorry typo. Point's the same though. Sufficiently high r and s will do the trick.

Many thanks ... It looks so crystal clear once you have the solution

Do you have a "special strategy" to find these sets of numbers ? I'm always encoutering problems when dealing with those types of problems (the list type).

Yeah, I put down D as well. Coundn't pick the right numbers.

Does anyone know of a better strategy for this one?

I picked A because of the following reasoning:
0<r<1
1<s<2

so r is a smaller no. than s

1. r/s ==> smaller no./larger no. should be < 1

2. rs ==> smaller no. * larger no. may be > 1 or < 1

3. s-r ==> larger no. - smaller no. may be > 1 or < 1