Mike is here with your Apex GMAT problem of the day. Today we are going to look at a percentage problem and we are going to break it down based upon a few characteristics. This is a very typical GMAT percentage problem. Let’s take a look at it:
A lemonade stand reported total sales of $36,700 last year. If the total sales for the year before was $28,000, approximately, what was the percentage increase in sales?
A. 3%
B. 28%
C. 30%
D. 45%
E. 66%
1. Approximately
So, first things first, the thing that you should hone in on immediately in this problem is this term “approximately”. Whenever you see the term you know that they’re not going to give you a precise answer, and so you are not on a hook for the precise answer. It should scream estimation to you!
2. Questions Tricks
If you take a look at the problem itself you see that they offer you two numbers that you will be comparing. But one of the interesting features is that they give you the more complicated, more ugly number, less round number, first and the other number, the 28,000, second. And this is designed to focus you towards the more exacting approach. When in fact, your optimal solution path is recognizing that the 28,000 is your base and instead of computing the differential, super math style, of you know 36,700 minus 28,000 and then putting it over the 28,000, the original number.
3. What If?
Instead, we want to play a “What If” and say okay, 28,000 is my base so what if I took 10% of it? That’s going to be 2,800. What if I took 20% of it? 5,600. What if I took 30% of it? And there’s your number right there. So, what we can see if it’s not immediately apparent from a scale perspective is that this big ugly number here is 30% higher. Even if we had that from the scale perspective. Even if we’ve recognized it’s about a one-third higher.
Notice there are two answer choices that are tightly clustered around that 30 percent. There is the 30% that’s our correct answer. Because the real number is somewhere around 31 percent and change. But there’s also that 28%, and so we need to get to some exacting level. And we do this by playing that “What If?” and saying: Okay, we can fit three blocks of 2,800 in and that gets us just below the target number that they give us in the problem.
4. Clustered Answers
This is a great problem to problem form. And you can play around with your mental map as well on it. Also, there’s a signal. It’s more of a subtle one and a little less reliable in the answer choices. On the one hand, you have the cluster of 28 and 30. And so, you can reasonably suggest that because these two numbers are close together and because we’re looking at estimation as a solution path.
The GMAT is testing our differentiation and our estimation skills. And that hones us into or narrows us down to a B vs. C situation. Other clusters that are here, that are less meaningful is the difference between A and C which is a factor of ten. But given that, and given our B vs. C once again, we are pointed towards a C answer. Now we have two different clusters that share C in common.
The GMAT does this a lot more often than you might think. And while it’s not always 100% reliable, it can be a very valuable tool. Especially when you’re short on time or need to make a decision on a problem where you don’t have a lot of uncertainty.
If you enjoyed this Percentage GMAT Problem, try out others: Combinatorics Problem