Data Sufficiency

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

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.

yes brother there can be several ways to do this question. And in fact an analysis can also solve this problem. however you can try which ever way is comfortable

we need relations between t1 and t2 & p1 and p2.

total cost would be p1(1+t1/100), p2(1+t2/100)
so .p1(1+t1/100)> p2(1+t2/100) ??
stmnt1- gives the relation between taxes, no info about p. so not sufficient
stmnt2- p1t1 > p2t2 not sufficient.

combining still not sufficient. problem is that we still don't know if P1 is greater than P2 or not.
hence E

if we take two statements together, there are still two possibilities.

So E.