We’ve looked at a lot of ways the GMAT can make Data Sufficiency questions more challenging (number properties, I’m talking to you!), but one type of DS question the GMAT likes to throw out there to really confuse unwary test-takers are value questions that ask about sums.
Say we had a question that asked, “what is the value of the sum of x and y?” Immediately, we have two possible ways that the statements could offer sufficiency: if they provided us with the ability to solve for x and y independently, and if they provided us with the ability to find the sum itself.
For questions like this, our “n equations for n variables” rule can get us into trouble. For these
“sum” questions, we have to remember that the sum itself is all we’re looking for. If a statement tells us that x + y = 8, then it’s 100% sufficient, even though we don’t know the exact values of x and y.
Let’s look a sample question:
If angle TXV = 40 and angle XTV is acute, what is the value of the sum of angles a and b?
(1) Triangle XYZ is equilateral.
(2) Triangle TVX is a right triangle.
Statement (1) tells us this is an equilateral triangle, so we know the value of each interior angle of XYZ is 60, and thus angle YXT = 20. Since a + 20 + 60 = 180, a = 100, but we still do not have enough information to find the value of b since we have no information about angle TVZ. Insufficient.
Statement (2) tells us that angle TVX = 90, and since angle TXV = 40, angle XTV = 50. Since a, b, and angle XTV share a straight line and are supplemental, the value of a + b must be 130. Sufficient.
The correct answer is (B).
Remember, treat any Data Sufficiency value question asking about sums with a little extra care and handling: the statements might be sufficient in unexpected ways!
Vivian Kerr is a regular contributor to the Veritas Prep blog, providing advice to help students better prepare for the GMAT and the SAT.