What we see: a Data Sufficiency question about parts of a total. Arturo spent $12,000 on three things: mortgage \(M\), real estate taxes \(T\) and home insurance \(I\). We must find \(T\).
Step 1. Write the one equation we have.
What we see: the three costs add to $12,000.
What it means: \(M + T + I = 12{,}000\). Three unknowns and one equation, so we need a statement that lets us pull \(T\) out by itself.
Step 2. Statement 1 alone.
What we see: taxes plus insurance were \(33\tfrac{1}{3}\) percent, which is one third, of the mortgage.
What it means: \(T + I = \tfrac{1}{3}M\). Put that into the total: \(M + \tfrac{1}{3}M = 12{,}000\), so \(M = 9{,}000\) and \(T + I = 3{,}000\).
What we do and why: we know taxes and insurance together, but not how the $3,000 splits. Taxes could be $1,000 or $2,500. Not sufficient.
Step 3. Statement 2 alone.
What we see: taxes were 20 percent of mortgage plus insurance.
What it means: \(T = 0.2(M + I)\), so \(M + I = 5T\).
What we do and why: put \(5T\) in place of \(M + I\) in the total: \(5T + T = 12{,}000\), so \(T = 2{,}000\). One value. Sufficient.
The trap: picking C. Statement 1 gives two clean numbers, $9,000 and $3,000, so it feels like the other statement is needed to finish. But statement 2 already compares taxes to everything else, which is all we need.
Faster way: a statement that compares the one part you want to the sum of all the other parts always gives that part when the total is known: here taxes are 1 share and the rest is 5 shares, so taxes are \(\tfrac{1}{6}\) of $12,000.
Takeaway: when you know the total, look for a statement that ties the part you want to "the rest." A statement that ties the other parts together leaves your part mixed in with something else.
Answer: B