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by arorag » Sun Jun 29, 2008 5:38 pm
Leo can buy a certain computer for p1 dollars in State A, where the sales tax is t1 percent, or he can buy the same computer for p2 dollars in State B, where the sales tax is t2 percent. Is the total cost of the computer greater in State A than in State B?
(1) t1 > t2
(2) p1t1 > p2t2
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by szapiszapo » Tue Jul 01, 2008 12:29 pm
Not so sure but I would say that answer is A (statement 1 sufficient, statement 2 not sufficient)

cA = cost in state A = p1(1+t1)
cB = cost in state B = p2(1+t2)

check on condition 2:
cA > cB translates into p1(1+t1)>p2(1+t2)
i.e. p1+p1t1 > p2+p2t2
i.e. p1t1 > p2t2 + (p2-p1)

(p2-p1) is different from zero hence [b]condition 2 is not sufficient[/b] alone as we would need to know if p2-p1 is >0 or <0


check on condition 1:
cB translates into p1(1+t1)>p2(1+t2)
i.e. p1+p1t1 > p2+p2t2
i.e. t1(p1+p1/t1)>t2(p2+p2/t2)
i.e. t1>t2*k, with k=p2(1+t2)/p1(1+t1)

we know from cA>cB that p1(1+t1)>p2(1+t2)
thus p2(1+t2)/p1(1+t1) < 1
i.e. k<1
and t1 is not > t2

Given that we can answer the question (the answer being no), [b]condition 1 is sufficient[/b]
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