June 25, 2012
How many times have you reviewed a question that you missed in practice and had that “face-palm” moment in which you realize that you missed something because you stopped too soon or solved for the opposite or just a portion of what the question was asking for? It happens too many times for most test-takers. So many of the mistakes made on the GMAT are avoidable errors. This is especially true on the simpler quantitative problems, because test-takers commonly let their guard down on the easier problems. They take the moment to breathe and end up walking straight into an easy error even though they understand the concept being tested.
Take this question for example:
There are 84 supermarkets in the FGH chain. All of them are either in the US or Canada. If there are 22 more FGH supermarkets in the US than in Canada, how many FGH supermarkets are there in the US?
There are two variables in this word problem, US supermarkets and Canadian supermarkets. First, many people default to “X” and “Y” as standard variables; however, if it is possible, strive to pick variables that better represent the items in the question because “X” and “Y” are easily confused at the end of the question and can easily lead to the “face-palm” answer choice. Let’s avoid that possibility here by using U and C as we translate the two equations in this word problem. As Lucas has mentioned previously, be systematic about how you unpack a word problem.
“There are 22 more FGH supermarkets in the US than in Canada.”
U = 22 + C
Also, “there are 84 supermarkets in the FGH chain.”
U + C = 84
Here’s how one could understand the math but still easily miss this question. Because the first equation already has “U” isolated, most test-takers will substitute that directly into the 2nd equation. While this is mathematically legal, immediately taking the most obvious and familiar route before thinking carefully about where you are headed in order to solve for US supermarkets leads right to the “face-palm” answer choice that is lying in wait.
(22 + C) + C = 84
22 + 2C = 84
2C = 62
C = 31
This seems fairly simple mathematically, and answer choice “B” is sitting there as a possibility; however, it’s not the answer to the actual question. Answer choice “B” represents the number of Canadian supermarkets instead of the asked for US supermarkets. You can see how this could be especially confusing if we were using just “X” and “Y” as the variables.
To avoid this potential situation with two variables, it’s usually best either to use combination if you are going to do the math or to backsolve starting with answer choice B or D as the number of US supermarkets.
In combination, we would want to make sure that the “C” can cancel out, leaving us with the desired “U” at the end.
U – C = 22 (first equation rearranged in line with the second equation)
+ ( U + C = 84)
2U = 106
U = 53, which is the correct answer
Let’s take a look at one more in which a simple problem can easily go awry if you don’t stay on your toes.
The officers of a local charity met together to address 500 invitations to an upcoming fundraising event. If they addressed 1/5 of the invitations in the first hour, and 3/8 of the remaining invitations in the second hour, how many invitations remained to be addressed after the first two hours?
As you work toward the asked for number of invitations left to be addressed after two hours, all of the answer choices in this question are numbers that you could get using the information in the question.
(1/5)500 = 100 –> the number addressed in the first hour and incorrect answer choice A
500-100 = 400 –> the number remaining after one hour and incorrect answer choice E
(3/8)400 = 150 –> the number addressed in the second hour and incorrect answer choice B
500 – 150 = 350 –> the number remaining if you only take hour 2 into consideration and incorrect answer choice D
500-250 = 250 – the correct answer and answer choice C!
While this problem is lower difficulty in terms of actual math content, there are plenty of opportunities for missteps built in. The big take-away from this information is that you must stay on your toes throughout the test and make sure that you double-check that you have solved for what the question is really asking. The test-makers build in opportunities for these missteps into many questions on the test, especially the quantitative questions with multiple steps. Always be systematic and deliberate as you drive towards the specific goal of the question.
If you ever find yourself in a “face-palm” moment as you prep for test day, and we’ve all had them, make sure that your action steps going forward include “confirm the answer every time”! Don’t give up points on test day because of a small misstep when you understand the underlying concept!
March 3, 2012
When most of my students start preparing for the GMAT, they are not very confident in their math ability for a variety of reasons. But, once in a while I will get a student that is very comfortable solving problems algebraically. On one hand, this is great. Algebra is an important skill on the GMAT and all students should master it before they take their test. However, there is a downside to this confidence. Many of these students do not want to learn, and do not spend time on, other strategies that can be useful to solve problems.
If you can find the correct answer to a question algebraically and do so in under two minutes, you can feel free to use algebra. But you also need to remember that you have other options to solve these questions and sometimes those other options will be faster. Just because it is possible to solve a problem algebraically does not mean it is in your best interest to do so.
With this in mind, it is important to think about all of the different ways a question can be solved when you are studying. By mastering a number of strategies you will be able to choose the one that will be fastest on a specific question and save time on test day. Thus, it is important to know different ways to solve problems no matter how good you are at any one of those options.
Try the practice problem below and, after you come to a solution, try it a second time but attempt to reach the answer a different way. You can check the explanation to see how this question can be attacked without doing any algebra.
A team won 50 percent of its first 60 games in a particular season, and 80 percent of its remaining games. If the team won a total of 60 percent of its games that season, what was the total number of games that the team played?
Since we want to work backwards to solve this problem, let’s start by considering our answer choices. Option (E) can be eliminated right away. Since we know that the team has already played 60 games, it is impossible for the team to play 30 games in total.
Next we need to decide which answer choice to assess first. Your best bet is to start with either choice (B) or (C), because, for example, if we test (B) and find it is too small, we know (A) is the answer without any additional work. Similarly, if we test (C) and it is too big, (D) must be the answer. When deciding between (B) and (C), we should go with the option that looks as if it will be easier, in this case that is (C), because it is smaller.
From the question stem, we know that the team won 50% of its first 60 games, which is 30 games. Choice (C) tells us that the team played 90 games, 60% of which it won. That means that the team won 54 games. To find this quickly, determine 10% of 90, which is 9, and multiply by 6.
In order to find how many of those 54 games were won after the first 60 games, subtract 30 from 54, which gives us 24. Thus, we know that during its remaining games, the team won 24 games. Additionally, we know that after the first 60 games, the team played 30 more games, which we found by subtracting 60 from 90.
Now we need to see if the team won 80% of its final 30 games. To determine this set up the fraction of games won over games played, which is 24/30. Simplify this to 4/5 and convert to a percent. 4/5 = 80/100 = 80%. Since this is the percent of remaining games won the question stem wants us to reach, we know that (C) must be the correct answer.