When looking at geometry problems on the GMAT, it’s important to take all graphs with a grain of salt (low fat, though). The graphs used on the GMAT are simply there to help visualize the problem at hand. No concerted effort is made for the graphs to be accurate or exact, and the graph should be evaluated based on what you know to be true, not on what you see or what the graph seems to imply. This all means that trusting your eyes on the GMAT is like trusting a car mechanic: you may have an honest mechanic or you may be getting taken for a ride!
When the question is dealing with triangles, it’s very easy to think that it must be one of the common figures you’re used to seeing. The triangle is likely either isosceles or equilateral, and there’s a good chance at least one of its angles is 90°. However, the triangle that looks equilateral could just as easily be 59°, 59° 62° (atomic protractors are still not allowed on the GMAT). If the facts don’t tell the story, you still can’t approximate from an arbitrary graphic. The graph may not purposely be trying to deceive you, but that doesn’t mean you can infer relevant information from it either.
As an example, let’s look at a data sufficiency question concerning a graph that looks like an equilateral triangle at first glance.
Is the triangle above equilateral?
(1) x = y
(2) z = 50
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
As stated, this triangle looks like all three angles are the same, but we need to see whether the facts confirm this observation.
Statement 1 tells you that angle x is equal to angle y. This is consistent with the notion that all three angles are the same, but it does not confirm it. For example, the angles could easily be 70 degrees for x, 70 degrees for y, and (180-70-70=) 40 degrees for z. If the statement allows for the case where the triangle is equilateral and the case where the triangle is not equilateral, then the statement must be insufficient by definition.
Looking at statement 2 on its own, it tells us that the angle z is 50 degrees. If we combined this with statement 1, we’d have all three measurements as z has to be 50 and x and y each have to be (180-50)/2 or 65 degrees. However, we do not put the statements together unless (2) is insufficient on its own. In this case, for the triangle to be equilateral, we know that all three angles must equal 60 degrees (anything less would be uncivilized). If angle z is 50 degrees, then regardless of the values of x and y, this triangle cannot be equilateral. Statement 2 on its own is sufficient and the correct answer choice is B.
There are two aspects worth noting here. The first is that, with both statements, we have more information than with statement 2 alone. Why is B the correct answer if the other statement adds more information? It is because the new information is irrelevant to the question being asked. Statement 2 answers the question on its own; there is no need to get the other statement. The other noticeable aspect is that the triangle looks exactly like an equilateral triangle, but answer choice B is confirming that it is not. Even if the answer looks like it should be yes, you have to let the math determine the correct answer.
Another interesting aspect to this problem is how close it could have been to having a completely different answer. If the question had asked “Is the triangle isosceles” instead of equilateral, the answer would have been completely different as statement 1 guarantees that two sides are equal, and statement 2 tells us nothing at all. Depending on the question being asked, the answer can change completely. On the GMAT, it’s important to get the right answer to the right question, and not the right answer to the wrong question.
Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam. After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.