Leo can buy a certain computer for p1 dollars in State A

[melguy]

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

Please help me with this problem. I am still unsure about Statement 2. As per my understanding the tax cannot be zero and all numbers must be positive. The question is asking about the cost i.e. total. So it must be that cost in State A is greater than cost in State B regardless of how small or large p1t1 is : Is there a logical conclusion we can come to without testing numbers?

Thanks

OA is E

[GMATGuruNY]

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

To save time, try to plug in combinations that satisfy both statements.

Case 1:
Let p� = 100 and t� = 20, so that p�t� = 100*20 = 2000.
Let pâ‚‚ = 100 and tâ‚‚ = 10, so that pâ‚‚tâ‚‚ = 100*10 = 1000.
A = p� + (t�% of p�) = 100 + (20% of 100) = 120.
B = pâ‚‚ + (tâ‚‚% of pâ‚‚) = 100 + (10% of 100) = 110.
Result:
A>B.

Since A>B in Case 1, the goal in Case 2 is to find values such that A<B.
In Case 1, p�t� = 2000.
To make A<B, try to increase pâ‚‚tâ‚‚ to a value just below 2000.

Case 2:
To goal is to find a combination such that A
Let p� = 100 and t� = 20, so that p�t� = 100*20 = 2000.
Let pâ‚‚ = 190 and tâ‚‚ = 10, so that pâ‚‚tâ‚‚ = 190*10 = 1900.
A = p� + (t�% of p�) = 100 + (20% of 100) = 120.
B = pâ‚‚ + (tâ‚‚% of pâ‚‚) = 190 + (10% of 190) = 209.
Result:
A<B.

Since A>B in Case 1, but A<B in Case 2, the two statements combined are INSUFFICIENT.

The correct answer is E.

Algebraically:

Total cost in A = p� + (t�% of p�) = p� + (t�/100)p�
Total cost in B = pâ‚‚ + (tâ‚‚% of pâ‚‚) = pâ‚‚ + (tâ‚‚/100)pâ‚‚

Question stem:
p� + (t�/100)p� > p₂ + (t₂/100)p₂ ?
p� + (p�t�)/100 > p₂ + (p₂t₂)/100 ?

When the statements are combined, we know that (p�t�)/100 > (p₂t₂)/100, but we cannot determine the relationship between the portions in red.
Thus, the two statements combined are INSUFFICIENT.

[Jeff@TargetTestPrep]

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

We are given that in State A a computer costs p1 dollars with t1 percent sales tax. Thus, the total cost of the computer in State A is:

(p1) + (p1)(t1)

We are also given that in State B a computer costs p2 dollars with t2 percent sales tax. Thus, the total cost of the computer in State B is:

(p2) + (p2)(t2)

We need to determine the following:

Is (p1) + (p1)(t1) > (p2) + (p2)(t2) ?

Statement One Alone:

t1 > t2

Statement one simply tells us that the sales tax rate is greater in State A than in State B. Since we have no information about p1 or p2, statement one is not enough information to determine whether (p1) + (p1)(t1) > (p2) + (p2)(t2).

Statement Two Alone:

p1t1 > p2t2

Statement two tells us only that the amount of sales tax for the computer is greater in State A than the sales tax amount in State B. Since we have no information about p1 or p2, statement two is not enough information to determine whether (p1) + (p1)(t1) > (p2) + (p2)(t2).

Statements One and Two Together:

Using our two statements, we can add together our inequalities and we have:

p1t1 > p2t2

+ t1 > t2

= p1t1 + t1 > p2t2 + t2

Although it may seem like we have enough information, we must remember that p1t1 + t1 > p2t2 + t2 is NOT the same as the inequality (p1) + (p1)(t1) > (p2) + (p2)(t2) in question.

We also could recognize that without knowing the selling price of the computer in the two locations, we can't answer the question. For example, if p1 = $100 and t1 = 8%, the cost of the computer will be $100 + $8 = $108 in State A; if p2 = $200 and t2 = 1%, the cost of the computer in State B will be $200 + $2.00 = $202. However, if p1 = $300 and t1 = 5%, the cost of the computer will be $300 + $15 = $315 in State A; if p2 = $100 and t2 = 4%, the cost of the computer will be $100 + $4.00 = $104 in State B. In the first scenario, State A's computer costs less than State B's computer. In the second, State B's computer costs less than State A's computer.

Therefore, we still don't have enough information to answer the question.

Answer: E