What percentage of steel workers in the country earns over $

One great way to look at this problem is to visualize it as a Venn Diagram. We have two overlapping groups: those steel workers who make over $37,000 annually (I will call them group “\(A\)”), and those who have a net worth above $200,000 (I will call them group “\(B\)”). There is an overlap between the groups, containing people who meet both criteria. I will call them group “\(M\)”. There is technically also a “neither” group (“\(N\)”): steel workers who do not meet either of the criteria. The total number of steel workers \((T) = A + B + N – M\). (Remember, when you add overlapping groups, you double count the mixed group, \(M\).)

The target for this problem is the percentage of steel workers who meet both criteria. (Notice the critical leverage word “also.”) This percentage is calculated by knowing the mixed group, \(M\), and dividing it by \(T\). Thus, we need to find a numerical value for \(\frac{M}{T}\).

Statement #1 tells us that 55% of all the steel workers in the country (\(T\)) fit into group \(A\). Mathematically, this means that \(A = (.55)T\). However, we cannot manipulate this equation to solve for \(\frac{M}{T}\), since it gives us no information on the mixed group, \(M\). Statement #1 is insufficient.

Statement #2 tells us that 12% of the steel workers with an annual income over $37,000 also have a net worth above $200,000. (Once again, notice the critical leverage word “also.”) Mathematically, this means that \((.12)A=M\). Again, this equation alone does not allow us to calculate \(\frac{M}{T}\), since it gives us no information on the total group, \(T\). Statement #2 is insufficient by itself.

However, when we substitute the first equation into the second equation, we get the equation \((.12)*(.55)*T = M\). There is no reason to do any more math, because it is easy to see that we can solve this combined equation for the term \(\frac{M}{T}\). The two statements together are sufficient, and the answer is C.

It might be worth noting here that we never actually able to solve for the individual values for \(M\) and \(T\). We don’t have to. We can solve for a chunk of an equation without needing to know the individual components. This is a concept I call “Chunky-quations” in my classes. The GMAT often gets you to assume that you need to know each piece, instead of just looking for a combined value. This is a classic GMAT trap.