Don't fall for the trap here. This question is not about the math. Many explanations of Quantitative questions focus blindly on the math, but remember: the GMAT is a critical-thinking test. For those of you studying for the GMAT, you will want to internalize strategies that actually minimize the amount of math that needs to be done, making it easier to manage your time. The tactics I will show you here will be useful for numerous questions, not just this one. My solution is going to walk through not just what the answer is, but how to strategically think about it. Ready? Here is the full “GMAT Jujitsu” for this question:
Many people spend too much time on Data Sufficiency questions because they think they need to solve to the bitter end. The question asks “
What was the median price of the three houses?” This is a "
Specific Value" question – a very common structure for Data Sufficiency problems. If you can think of two situations (or two variable inputs) that are consistent with all of the problem’s constraints but come up with different answers to the question, you know a statement is insufficient. In my classes, I call this strategy “
Play Both Sides.”
Let’s analyze each statement, and you will see what I mean. Statement #1 tells us that Tom’s house cost
\($110,000\). Trying to “mathematize” this into a formula is unnecessary. We just need to think of two situations that would give us different answers to question. The price of Tom’s house is below the average of
\($120,000\), but we don’t know the values of the other two houses, including the value of the home in the middle. Remember,
median is the middle value of a set of numbers when arranged in ascending order. Now, we go through the headache of inventing specific numbers here (for example, if the three homes were valued at
\($110,000\),
\($120,000\), and
\($130,000\), the average would be
\($120,000\) – but so would three homes valued at
\($1\),
\($110,000\), and
\($249,999\). The median values of these two sets are clearly different.) However, coming up with concrete values here is is more work than we need to do. We don’t need to do all the math to show that there are multiple possible solutions. We just need to know that multiple possible solutions COULD exist. Statement #1 is insufficient.
Statement #2 tells us that Jane’s house cost
\($120,000\). The primary bait behind this statement is to trick you into turning your brain off. Statement #2 is very similar in appearance to Statement #1. The two statements sound like they are "playing the same game." But when you see
similar statements in Data Sufficiency questions, you should start by looking at how the statements are
different, and see if those differences are meaningful. You see, if Jane’s house is equal in value to the average, then it must be the median value in a set of three homes. We don’t know what the other two homes are valued at, but we don’t need to know. If they were all the same value, the median value would be
\($120,000\). If the other two homes had different prices, then the only way to get an “average” would be to have one home be
lower than
\($120,000\) and one home
higher. Either way, the median home stays the same. Statement #2 is totally sufficient.
The answer is “B”.Now, let’s look back at this problem through the lens of strategy. This question can teach us patterns seen throughout the GMAT. First, notice that this problem is much more about
logic and
critical-thinking than it is about math. This is especially true with problems involving statistics. Such problems trap you into thinking that you need all the information. But you only need enough information to
prove or
disprove sufficiency. If you can think of two situations (or two variable inputs) that are consistent with all of the problem’s constraints but come up with different answers to the question, you know a statement is insufficient. Second, similar-looking statements in Data Sufficiency questions often bait you into thinking that you must treat each statement in the exact same way. Rather than thinking linearly and assuming because they sound the same that they play the same game, the trick is to leverage the
differences between the statements. That is how you think like the GMAT.
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Aaron PondVeritas Prep Teacher of the Year / Professionally mentoring GMAT students since 2006 Visit me at https://www.veritasprep.com/gmat/aaron-pond/ if you would like to learn even more "GMAT Jujitsu"!