Bunuel wrote:
Orange08 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?
10
(1) t1 > t2
(2) p1t1 > p2t2
I chose B. However, OA is different. please explain.
You can solve this question algebraically, but think number plugging is better this time.
Total cost = p*(1+t/100).
(1) \(t_1>t_2\) --> no info about the prices. Not sufficient.
(2) \(p_1*t_1>p_2*t_2\) --> amount of tax in $ is more in A than in B. Now if \(t_1>0%\) and \(t_2=0%\) then given statement works for any prices of computers (any positive \(p_1\) and \(p_2\)). So not sufficient, to answer whether total cost of the computer greater in State A than in State B.
(1)+(2) Again if \(t_1=10%>t_2=0%\) (statement 1) then \(p_1*t_1>p_2*t_2=0\) (statement 2), but from this we can not establish relationship between total cost of the computer in State A and in State B. For example if \(p_1=p_2\), then total cost in A would be higher than in B (because total cost in B would be just \(p_2\), as \(t_2=0%\) and in A would be higher than \(p_2=p_1\) as \(t_1>0%\)),
but if \(p_1=1\) and \(p_2=100\) then total cost in A would be lower than in B (because total cost in B would be \(p_2=100\), as \(t_2=0%\) and in A would be \(p_1*1.1=1.1\) as \(t_1=10%\)). Not sufficient.
Answer: E.
Bunuel -
I have 2 things here:-
1. Why are we assuming tax is over the price? According to me, price should be inclusive of tax since question mentions that that "Leo can buy at P1", i.e. he would have to pay P1 cash to buy the computer.
2. Also, why are we assuming base price (i.e. exclusing sales tax) of the two computers separate in two states? The question mentions that the price of the same computer in other state. So, according to me, since the computer model is same, the base price in both states is same and the sales tax rates are different leading to differen overall price P1 and P2.
When I take these two conditions, my answer comes out to be D.
I think the question is ambiguous.