DS Question from OG 12

[poojaswamy]

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 rate is t2 percent. Is the total cost of the computer greater in State A than in state B?

1. t1 > t2
2. p1t1 > p2t2

This is how I approached this problem.

Need to check if p1+p1t1/100 > p2+p2t2/100

Statement 1 - IS
Stmt 2 - IS

1+2 - t1>t2, p1t1>p2t2 implies p1>p2 (since we definitively know t1 and t2 are positive). So, we have p1>p2 and p1t1>p2t2, implying p1+p1t1/100 > p2+p2t2/100.

Can mgmat staff please help?
OA - E

[RonPurewal]

t1>t2, p1t1>p2t2 implies p1>p2 (since we definitively know t1 and t2 are positive).

this is not true.
for instance, 2 > 1 and (3)(2) > (4)(1) does not imply that 3 > 4.

the converse is true -- i.e., if you had t1 > t2 and p1 > p2 (all positive) then you would know that t1p1 > t2p2 -- but you can't do that the other way around.

[poojaswamy]

Didn't expect to get a response on a weekend. You guys ROCK!!! Thanks Ron :)

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 rate is t2 percent. Is the total cost of the computer greater in State A than in state B?

1. t1 > t2
2. p1t1 > p2t2

This is how I approached this problem.

Need to check if p1+p1t1/100 > p2+p2t2/100

Statement 1 - IS
Stmt 2 - IS

1+2 - t1>t2, p1t1>p2t2 implies p1>p2 (since we definitively know t1 and t2 are positive). So, we have p1>p2 and p1t1>p2t2, implying p1+p1t1/100 > p2+p2t2/100.

Can mgmat staff please help?
OA - E

[jnelson0612]

:-)