HSPA wrote: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
Question: Is A>B?
We can plug in values that satisfy the conditions given.
Statement 1: t1 > t2
No information about p1 and p2, so no way to compare A and B.
Insufficient.
Statement 2: p1t1 > p2t2
Let p1 = 100 and t1 = 20, so that p1t1 = 100*20 = 2000.
Let p2 = 100 and t2 = 10, so that p2t2 = 100*10 = 1000.
A = p1 + (t1% of p1) = 100 + (20% of 100) = 120.
B = p2 + (t2% of p2) = 100 + (10% of 100) = 110.
A>B.
Let p1 = 100 and t1 = 20, so that p1t1 = 100*20 = 2000.
Let p2 = 110 and t2 = 10, so that p2t2 = 110*10 = 1100.
A = p1 + (t1% of p1) = 100 + (20% of 100) = 120.
B = p2 + (t2% of p2) = 110 + (10% of 110) = 121.
A<B.
Since A>B in the first case and A<B in the second case, insufficient.
Statements 1 and 2 together:
The combinations used under statement 2 also satisfy statement 1, since in each case t1 > t2.
Thus, even when both statements are satisfied, it is possible that A>B and that A<B.
Insufficient.
The correct answer is
E.
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