3 Better Ways to Solve GMAT Problem Solving Questions
Today’s post comes from Eliza Chute who has been tutoring both the GMAT and the LSAT for over a year, in addition to running a GMAT prep website with course comparisons and study advice. She will be starting her JD/MBA next fall at NYU through the Jacobson Leadership Program in Law and Business. Prior to her tutoring career, Eliza spent several years in Southeast Asia training local activists and entrepreneurs on human rights, environmental studies and social entrepreneurship.
If you are looking at a problem solving question and thinking about tackling it in a long, roundabout way, then you are probably looking at it wrong. The questions are written in such a way that it seems like there is only an extremely complicated way of doing things, but in reality there is always a simpler way. So, before you start going into that five-minute calculation, stop and think about if there is a quicker way to do things.
1. Use what you’re given
The GMAT is multiple choice, so there is only a finite number of solutions to pick from. If those choices are far enough away from each other, then you may only need to estimate. Take, for instance, this problem:
What is 26% of 4/17 of 850?
These answers are fairly spread apart, so you don’t have to do the entire calculation, which would be unnecessarily complicated and time consuming. Twenty-six percent is a little over 1⁄4 and 4/17 is a little under 4/16 or 1⁄4, so you can just take 1⁄4 of 1⁄4 of 850, which is 1/16 of 850 or approximately 53. There is no number that is anywhere near that except for B, so we know that is our answer.
2. Pick a convenient number
Another strategy that might get you to the answer faster than simply doing the problem outright, is plugging in numbers. This might make it easier to visualize the problem and help you work through it faster. If you are struggling with a GMAT problem and are having trouble visualizing the problem, try replacing the unknowns with a value. For example, take a look at this problem.
To practice law in their state, the third year law students at Western University have to pass the bar examination. If 1/3 of the class opted not to take the bar examination and 1/4 of those who did take the test, did so and failed. What percent of the 3Ls will be able to practice law in their state?
You could try to solve this problem outright; however, an easier way might be to just pick a convenient number for the class and then use it to solve the equation. It’s important to choose your number carefully and strategically. Picking 5 for this problem wouldn’t work because you can’t take 1/3 out of 5 evenly. A better number is one that both 3 and 4 can go into, like 12. If the class has 12 people in it and 1/3 don’t take the test, that means 4 don’t take it and 8 do. Of those 8, 2 fail, so 6 in total are able to practice. The answer is asking for the percentage, so 6/12 is 50%.
3. Test answer choices
Another way to quickly answer questions when you are stumped is to test answer choices. You are only given five, so sometimes this will get you to the correct answer faster than doing the work to multiply the problem out.
You can rent DVDs at a local video store for $5.00 per movie without a membership. However, if you purchase a membership for $7.00 per month, you can rent DVDs for $2.00 a piece. What is the minimum amount of DVDs you would have to rent to make it worth it to purchase the membership.
Because this question is asking for the minimum amount, you can start testing at the bottom and work your way up. Once you find a value where the membership costs less than the non-membership, you have found your answer.
(A) with the membership it’s $9 and without it’s 5, so this isn’t our answer
(B) with the membership it’s $11 and without it’s $10, so also no
(C) with the membership it’s $13 and without it’s $15, so now we have found
The other way to have done this would have been to create an algebraic equation, set the two sides equal to each other and solve for x, then figure out the next value, like so:
7 + 2x = 5x
7 = 3x
x = 7/3 or 2 1/3
We could then deduce that the right answer is 3 because you can’t rent half a DVD.
However, with problems like these, it’s often faster to simply check answers, and at the end of the day, we want to get though the problems in the quickest way possible.
Another way to ensure that you are working your way through problems as quickly as you can is to keep numbers in their simplest form (i.e. primes). This way, you know when you can quickly eliminate common factors to figure out the answer. When you see a problem like this:
91x = 143*70
you might be tempted to multiply out 143*70 and then divide by 91. However, this isn’t the fastest way to do that. If we reduce it to primes, we will see that the problem is actually
13*7x = 11*13*7*10
We can then eliminate the 13 and the 7 from both sides and we know immediately that x is 110. When you are working through complicated problems that involve a lot of multiplication, don’t immediately try to multiply those numbers out. Keep them in their most basic forms while working through the problem.