One reason GMAT math problems can be hard is that the test writers try to trick you. After writing a question and choosing one answer choice to be the correct answer, test writers have four answer choices left to fill. One of the questions they ask at this point is whether there are any numbers that would make good trap answers. GMAT test-takers as a whole are predictable (so are most groups of people as a whole) and it’s not hard for the test writers to come up with some answers that will be very tempting. Part of your job in preparing for the GMAT is to become less predictable and less subject to these temptations. Let’s tackle a few examples.
The price of a jacket is reduced by 25%. During a special sale the price of the jacket is reduced another 10%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?
So what’s the answer here? If 35 looks like a good option to you, you’re in good company. It seems that a 25% discount followed by a 10% discount should total a 35% discount. But if the question were really that easy it wouldn’t be on the GMAT. This is where test-taking savvy has to kick in. You aren’t going to spend your time on the GMAT adding together two numbers that appear in the problem and getting the correct answer. That’s way too easy. 35 is a trap answer, and you need to train yourself to spot trap answers. So what’s the real answer if it’s not 35?
Let’s make this more concrete and give the jacket a price. For simplicity, call it a $100 jacket. A 25% discount will be $25, so now we have a $75 jacket. Next, another 10% is taken off. 10% of 75 is 7.5, so the new price is 75 − 7.5 = 67.5. After the two discounts the jacket costs $67.50. (Now you can see why 35% is incorrect. The two discounts can’t simply be added, because the second one is being taken from a different base number (75) than the first one (100) is.) To get back to $100 we have to raise the price $32.50. Now we need to use the percent change formula:
What else you can do inside qs leap ?
Percent change = . In a percent increaseproblem, the “original” number will be the smaller one, so our formula is . We don’t need to do the full calculation because is a little less than one half, and the only answer that’s in the ballpark is 48% in Answer C. As you can see, there are a lot of steps to this problem, and anyone who blithely picks 35 and moves on is missing all the important stuff.
Let’s look at another example.
Vivian drives to her sister’s house and back. She takes the exact same route both ways. On the trip out she drives an average speed of 50 miles per hour. On the trip back she drives an average speed of 70 miles per hour. What is her approximate average speed for the round trip in miles per hour?
Does anything look tempting here? Something that seems logical, but is perhaps too good to be true? The trap answer, of course, is 60. It seems to make perfect sense — half way between 50 and 70 — but it’s just too easy. No matter how much you want to pick it, you have to tell yourself that if the problem could be solved that easily it wouldn’t be on the GMAT. So 60 is out. What else can we eliminate?
Common sense should tell you that answer can’t be 50 or 70. You can’t drive there at 50, come back at 70, and average 50 for the whole trip, for example. That makes no sense. It has to be somewhere between those numbers. Let’s look at our remaining answers, 58.3 and 61.7. One of these is closer to 50 and one is closer to 70. So apparently one of these trips — either the 50mph trip or the 70mph trip — has had a greater effect and is “pulling” the average speed closer to itself. Which one? When dealing with problems about rates, there are three parts to consider: rate, distance, and time. We know the rates here. The distance is the same for each trip. The determining factor, therefore, is time. It takes longer to make the trip at 50mph than at 70 mph, so Vivian spends more time at that speed. This means the average will be closer to 50 than 70, and the answer is B.
Another way to solve this problem is to plug a distance into the problem. Because the trip is the same distance each way it doesn’t matter what you choose — the answer will be the same no matter what. Mathematically, however, it will be much easier if you pick a number that is divisible by 50 and 70. So let’s make this a 350 mile trip. That means it will take Vivian 350 ÷ 50 = 7 hours to drive there, and 350 ÷ 70 = 5 hours to drive back. That’s a total of 12 hours to drive 700 miles. Thus, her average speed for the round trip is 700 ÷ 12 = 58.3.
Keep an eye out for answer choices that are too simple. If you remember that the GMAT is going to make you work for answers, you’ll avoid falling for the traps that ensnare so many test-takers.