If |r| |s|, is r s?

Question

If |r|>|s|, is r>s?

(1) r>0
(2) s>0

Bunuel · Accepted Answer

If |r|>|s|, is r>s?

|r|>|s| means that r is further than 0 than s is. We can have the following 4 cases:

--r--s--0--------
--r-----0--s-----
-----s--0-----r--
--------0--s--r--

(1) r>0. We have case 3 or 4. In both of them r > s. Sufficient.

(2) s>0. We have case 2 or 4. r can be more than s (case 4) as well as less than s (case 2). Not sufficient.

Answer: A.

Abhishek009 · Answer

A different approach

Consider the problem this way -

Option (1)

Plug in some values -

r = 2 { r has to be a +ve integer > 0 ; because it is stated r>0 }

s = Can be any number less than 2 { It be any number less than equal to 1 }

So, we can say r>s.....
 
 Option (2)

Plug in some values -

s = 1 { s has to be a +ve integer > 0 ; because it is stated s>0 }

r = Can be any number less than 1 { It be any number less than equal to 0 ; so it can be negative }

Now we can not say r > s

Hope this helps !!
Please feel free to revert in case of any Doubt

Abhishek

If |r| > |s|, is r > s?