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by sumasajja » Fri Jul 22, 2011 5:03 pm
if 0<st<1
then which of the following can be true?
a) s<-1 and t>0
b)s<-1 and t<-1
c)s>-1 and t<-1
d)s>1 and t<-1
e))s>1 and t>1
usually such problems take more time two solve for me, is there a easy procedure that must be followed to get fast at these problems?
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by goalevan » Fri Jul 22, 2011 5:20 pm
With CAN be true problems, it's often best to eliminate answers first if possible before testing numbers.

In this case, with 0 < st < 1 it follows that st > 0, so s and t must have the same sign. You can immediately knock out answer choices A and D.

If s < -1 and t < -1, then the product must be greater than 1. Knock out answer choice B.
If s > 1 and t > 1, then the product must be greater than 1. Knock out answer choice E.

This leaves only answer choice C, the correct answer. We can plug s = -1/10 and t = -2 to verify that indeed, -1/10 * -2 = 1/5 is between 0 and 1, so it CAN be that 0 < st < 1.