thinkvision wrote:
Statement (1) says that total sales were $1,500,000 but provides no breakdown of sales between the two products. So, 1,500,000 = 5a + 4b and Cost = 3a + 3b + 500,000. There are now two equations and three variables: Cost, a, and b. Thus, Statement (1) is insufficient; eliminate (A) and (D).
Your solution was correct until this point, but as soon as you start counting equations and unknowns, you are no longer answering the question that was asked. The question does not ask if you can solve for a or b individually -- only then would counting equations and unknowns even potentially be helpful (but with 3 unknowns, the rules are much more complicated than with only 2 unknowns). Instead the question asks merely whether the company made a profit. And if that's the question, the numbers genuinely matter. For example, if we knew the company's revenue was only $9 (one product of each type), the company clearly could not have covered their $500,000 fixed cost. Then we'd be sure they took a loss. If instead the company's revenue was $40 trillion, then since they profit on each sale, then no matter how the sales broke down between products A and B, the company would easily cover their $500,000 fixed cost, and we could be certain they made a profit.
We know the company profits $2 for each unit of product A sold, and $1 for each unit of product B. Their revenue is 5a + 4b. Using both Statements, we can consider two extreme scenarios. Their revenue from A was greater than their revenue from B. It's possible all of their revenue was from A. In that case, 5a = 1,500,000, and a = 300,000. We then know they make a profit of 2a = $600,000, which would indeed cover their $500,000 fixed cost. But it's also possible that their revenue from A is almost equal to their revenue from B. So it might be that their revenue from A is slightly greater than half of 1,500,000. Say it's exactly half, so 5a = 750,000. Then a = 150,000. We'd also have 4b = 750,000, and b = 187,500. Since their profit is 2a + b dollars, the profit is $487,500 (so would be negligibly greater than that if revenue from A is strictly greater than that from B). So it's possible, but only just, that the company fails to cover their $500,000 fixed cost, and the answer is E. But if the numbers were changed just slightly -- if the revenue were slightly higher, say, or the fraction of the revenue from A was slightly higher -- the answer would be C, or possibly A, depending on the details.
Possibly the best advice I can give to a GMAT test taker who is counting equations and unknowns to solve DS questions is to stop counting equations and unknowns. I've broken down large pools of official DS questions by difficulty level, and have then evaluated how often one would get a right answer by unthinkingly counting equations and unknowns. Even at the medium level, you only get a right answer 1/3 of the time (and the same is true at the hard level), which is almost like guessing randomly when you consider that in DS one or two answer choices can often be ruled out instantly. If you're reading prep company material that recommends the strategy, I'd advise finding better material to study from.