When looking at questions on the GMAT, it’s very easy to fall into the mentality that there is only one correct answer. If I’m searching for some number xyz multiplied by another number abc, I don’t necessarily know the answer, but I know there’s only one value that will correctly satisfy the equation. The entire concept of multiple choice is predicated on having only one correct answer (also on knowing the alphabet), so it seems counter-intuitive that two values could both be the correct answer.
However, consider the simple case of any quadratic function. If X^2 = 9, then either the value 3 or the value -3 will work. If such a choice were given on a GMAT question, then the answer choices will contain either -3 or 3, but never both (the exclusive or: XOR). If the answer choices were, for example:
This distribution would indicate that either answer A or D is correct. Examinees wouldn’t know which choice to pick, since either answer would be correct. The answer choices must look something like either:
A) -5 A) -3
B) -1 B) -1
C) 0 or C) 0
D) 3 D) 2
E) 9 E) 4
Each list has only one correct answer among the choices given. The trick is to not figure that the answer is 3, look through the list without 3 on it and begin to doubt yourself over everything (did I remember to lock the door when I left home this morning?). If the answer choice you found is not among the choices listed, that doesn’t necessarily mean that your math is faulty. It’s entirely possible that another answer that also works is on the list, so check for other options before doubting your work completely.
Let’s review a question that has two answers but isn’t as obvious as a quadratic equation:
On the number line, if w > x, y is the midpoint between w and z, and x is twice as far from z as it is from w, then (w – y) / (z – x) could equal which of the following?
This question can be solved in a couple of different ways, but the easiest is probably to visualize it with a number line. Let’s start by arbitrarily putting x and w, where w has to be bigger than x. The number line goes from – infinity to infinity (and beyond!)
The next variable is z, and the only instructions we are given is that x is twice as far away from z as it is from w, which means z can easily be near the beginning of the number line.
z x w
Using this z, we know that y must be the midpoint between x and z, so let’s choose arbitrary small values that satisfy the conditions and plug them into the given equation to see what we get. I will define x as 1 and w as 3 and put the other numbers in between in order to only get integers.
z y x w
-3 0 1 3
Picking x to be 1 and w to be 3 gives a gap of two. Z is twice as far from x so it has to be four away from 1 (making it -3). Y is the halfway point from -3 to 3, so it is 0.
The equation (w – y) / (z – x) using the values above is (3-0) / (-3-1). This gives us -3/4. However, if we go back through the answer choices, -3/4 is not on the list. However, this is not because the math was incorrect or a mistake was made, there simply was another option for z on the number line.
Since z must be twice as far from x as from w, z can simply be further along the number line on the positive axis. Let’s redefine the original z as z1 and this new one as z2:
z1 y1 x w y2 z2
-3 -1 1 3 4 5
Z2 needs to be twice as far from x as it x is from w, so z2 must be 5. Y2 is the midpoint between 3 and 5, so it must be 4.
Now if we plug in the z2/y2 values into the equation (w – y) / (z – x), we get (3-4) / (5-1), which is -1/4, or answer choice B.
On the GMAT, it’s important to note that some answers can be correct, but not possible choices because another answer choice is also correct. Had the answer choice -3/4 been an option, many test takers would have chosen it and the other half would have opted for -1/4. Both answers are correct and neither is better than the other, but there is a conflict between them that multiple choice can’t easily solve.
One of the correct answers will be omitted because, on the GMAT (as in Highlander), there can be only one.
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.