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by Oxana » Fri Sep 26, 2008 6:32 pm
what is the shortest way to solve this

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

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

a. I only
b. II only
c. III only
d. I and II
e. I and III


the way I solved it is very time consuming

the ans is A
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by cramya » Fri Sep 26, 2008 6:55 pm
strictly my startegy for must be true questions:

Pick extreme values from both intrevals and test.

Eg: .001 and 1.99

II. rs
III. s-r

can easily be ruled out and r/s will definitely be 1 (I also tested out the case where r value is maximum and s value minimum to maue sure it will be true

Eg: .99 and 1.0
1.0/.99 = 10/9.9 > 1

I am not sure of an algebric way though.
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by cramya » Fri Sep 26, 2008 6:57 pm
Correction to my previous post:

Eg: .99 and 1.0

.99/1.0 = 9.9/10 < 1
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by stop@800 » Sat Sep 27, 2008 3:21 am
r lies betwen o and 1
s lies betwen 1 and 2

r/s
a no between 0 and 1 is divided by a no between 1 & 2
it will always be less than 1
bcoz

r is < 1
and any division to r by a no > 1 will not increase its value





rs
this can v easily be >1 if u look at range of both
so out





s-r
again the difference can vary from 1.99999999 to 0.0000000001
so out


Ans is A

Hope it helps
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