GMAT Instructor
Joined: 01 Jul 2017
Posts: 89
Location: United States
Concentration: Leadership, Organizational Behavior
Re: Did the sum of the prices of three shirts exceed $60?
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05 Nov 2018, 13:49
Let's talk strategy here. 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 get to the bitter end. The question asks “Did the sum of the prices of three shirts exceed $60?” This is a “Yes/No” question – a very common structure for Data Sufficiency problems. The fundamental trap for problems like these is to bait you into thinking that you actually need to solve for every value. You don’t. As soon as you have enough information to conclude that a statement is either sufficient or insufficient, you can move on. For “Yes/No” questions, 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 the “price of the most expensive of the shirts exceeded \($30\).” Trying to “mathematize” this into a formula is unnecessary. We just need to think of two situations that would give us different answers to the “Yes/No” question. Given the information in Statement #1, is it possible that the prices of the three shirts exceeds \($60\)? Sure. If the most expensive shirt exceeded \($30\), it is easily possible that that shirt was over \($60\) by itself. We can answer “Yes”. Is it possible the three shirts didn’t exceed \($60\)? Sure. If the most expensive shirt was \($31\), and the other shirts were free, they would sum to well less than \($60\). Since we can answer both “Yes” and “No”, Statement #1 is insufficient.
Statement #2 tells us that the “price of the least expensive of the shirts exceeded $20.” 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. It sounds like it is 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 the “least expensive” shirt exceeded \($20\), then we can’t get any free shirts. Every shirt must cost more than \($20\). And since the problem tells us that we are buying “three shirts”, then the total cost must be greater than \(3*($20)\). The price must exceed \($60\). 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. With “Yes/No” questions, a great tactic that you can often use is to plug in easy, hypothetical values that provide different answers to the question. Naturally, those values must follow the constraints inside the question, but if you can do this, you can “Play Both Sides” and disprove sufficiency. Second, similar-looking statements in Data Sufficiency questions often bait you into thinking that you must solve each statement in the exact same way. The trick is to leverage the differences between the statements, rather than thinking linearly and assuming because they sound the same that they play the same game. And that is how you think like the GMAT.