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rishab1988
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Statement 1: t1 > t2rishab1988 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 in State B, where the sales tax is t2 percent. Is the total cost of the computer greater in State A than in in State B
1, t1>t2
2, p1t1>p2t2
Tells us nothing about p1 or p2. Insufficient.
Statement 2: p1*t1 > p2*t2
Let's plug in different sets of values that satisfy statement 2 in order to see whether in each case State A > State B.
Let p1 = 100 and t1 = 20. Then p1*t1 = 100*20 = 2000.
Let p2 = 100 and t2 = 10. Then p2*t2 = 100*10 = 1000.
Statement 2 is satisfied because 2000 > 1000.
Cost in State A = 100 + .2*100 = 120.
Cost in State B = 100 + .1*100 = 110.
State A > State B.
Now let's try to plug in values so that State A < State B. Let's increase p2 just a bit and keep all the other values the same.
Let p2 = 110 and t2 = 10. Then p2*t2 = 110*10 = 1100.
Statement 2 is still satisfied because 2000 > 1100.
Cost in State A = 100 + .2*100 = 120.
Cost in State B = 110 + .1*110 = 121.
State A < State B.
Since it's possible that State A > State B and that State A < State B, insufficient.
Statements 1 and 2 together: t1 > t2 and p1*t1 > p2*t2
The two sets of values that we plugged in above satisfy both statements because in each case t1 > t2 and p1*t1 > p2*t2. Thus, even when we plug in values that satisfy both statements, it's possible that State A > State B and that State A < State B. Insufficient.
The correct answer is E.
