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
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient
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to solve this one we need relations between t1 and t2 & p1 and p2. total cost would be P1+P1t1/100, P2+P2t2/100.
1-> gives the relation between taxes, no info about p. so not sufficient
2-> with this statement, either p1, t1 > p2, t2 OR p1, t2 > p2, t1 OR t1, t2 > p1,p2 [but not p2, t2 > p1,t1]. so there are lot of possibilities. not sufficient.
E
Answer is (E).
E.
Assuming that the tax is in addition to the price paid for the computer then the question can be rephrased as is p1 (1+t1) > p2(1+t2) ? Which can be simplified to is p1 + p1 t1> p2 + p2 t2 ? So we need to know the ratio of purchase prices as well as the ratio of the amount of tax to be paid.
Statement 1) Insufficient. This tells us that sales tax % is greater for t1 than t2, but nothing about the purchase price.
Statement2) Insufficient. This tells us that the amount of tax paid for 1 is greater than 2, but it does not tell us purchase value. ie. If P1 is 100 and t1 is 10% and P2 is 50 and T2 is 5% then p1t1 >p2t2 (10>2.5) and the total cost of the purchase would be greater for 1 then for 2 (110>52.5). However, if p1 is 100 and t1 is 10 and p2 is 150 and t2 is 5 then p1t1> p2t2 (100*10%)>(150*5%) . . .10>7.5 however, 100+10 is not greater than 150+7.5.
Togeather) Insufficient. It is the same example as stated for the rebuttal of statement 2.
E
E
E
E
E.