Re: If 0 < r < 1 < s < 2. Which of the following must be less than 1.
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01 May 2022, 09:45
Notice that we are asked "which of the following MUST be lees than 1, not COULD be less than 1. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
Given: 0<r<s --> divide by s (we can safely do this since we know that s>0) --> rs<1, so I must be true;
II. rs: if r=910<1 and 1<(s=109)<2 then rs=1, so this statement is not alway true;
III. s-r: if r=0.5<1 and 1<(s=1.5)<2 then s−r=1, so this statement is not alway true.
Answer: A (I only).