P + 2T = 6.25
So we need "T".
Statement (1) gives us P = 3T. Between the original equation and statement (1), we have 2 variables and 2 distinct equations, so we'd be able to solve for either variable. SUFFICIENT.
(For the record, we don't need to actually solve, since it's DS, but if we did plug in 3T for P into the original equation to get 3T + 2T = 6.25, so 5T = 6.25, so T = 1.25
Statement (2) gives us 6T + 3P = 18.75. At first glance, this looks like it would be sufficient because we'd now have 2 variables and 2 distinct equations. But wait a second! This equation is not DISTINCT from the P + 2T = 6.25 we had originally.
If you take 6T + 3P = 18.75, divide both sides by 3, you'd have 2T + P = 6.25, same as P + 2T = 6.25. So statement (2) doesn't actually give us any information beyond what we already knew from the original problem. INSUFFICIENT.
(If you even tried to solve for either variable here, everything would cancel out and you'd end up with 0=0, which isn't helpful for anything)
Generally speaking, however many variables you have is equal to the number of distinct equations you'd need to solve for each variable, but that's assuming that you've simplified each equation as much as possible, and you do have to check that the equations are actually DISTINCT.
Gene Suhir
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