Oxana wrote:what is the best approach for problems like this one:

if 0<R<1<S<2, which of the following must be less than 1

I. R/S
II. R*S
III. S-R

Only I should be true.

R is greater than 0 and less than 1
S is greater than 1
The denominator is greater than numerator, therefore it wil always be less than 1

II . R*S can be greater than 1 because S is greater than 1

III. S-R = if S is 1.5 and R is .5 then S-R = 1 which is equal to 1.

Therefore only the First Statement Should be True.

I am not sure of what the best approach is, but I approach these kind of problems by listing down the immediate next value to the condition and then plugging in those values in the expression

Like here
Rmin = 0.01
Rmax = 0.99

Smin = 1.01
Smax = 1.99

now Solve with choose values that opposes the result, these values would always give most perninent results like
I 99/101 is always less that 1
II R*S can be > 1
III S-R can also be > 1

Hence only I is close to correct

Dont know if its the best approach or not.

Pick numbers that are easier to work with to and see if choices get eliminated.

If 2 are still true pick numbers from the extreme(low-high end) and test it out.