Use Smart Numbers to Speed Up Your GMAT Quant
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Are you having trouble finishing GMAT Quant word problems within two minutes? Here’s a technique that will help.
How Do I Know to Use Smart Numbers?
First of all, this technique is only for Problem Solving problems. It won’t work on Data Sufficiency.
It also doesn’t work on every Problem Solving problem. There are two scenarios where smart numbers will work:
- The answer choices are given in terms of a variable, not a number.
- The answer choices are ratios, percents, or fractions.
In both scenarios, the clues are in the answer choices. This means you have to build a new habit. From now on, you have to read the answer choices before you choose an approach. This will feel strange at first. If you’re anything like me, you’ll want to start writing down variables and equations before you even finish reading the problem, let alone the answer choices.
The problem is, once you’ve started writing down a bunch of algebra, you’ve already committed yourself to doing the problem with algebra. But algebra isn’t usually the smartest approach on these problems. The GMAT doesn’t give you enough time to test out an algebraic approach, then start over with smart numbers. Read the answer choices early, and start with smart numbers.
How Do I Do It?
It’s a little easier to apply smart numbers when there are percents, fractions, or ratios in the answer choices, so we’ll start there. Here’s an example problem:
Team A and Team B are raising money for a charity event. The ratio of money collected by Team A to money collected by Team B is 5:6. The ratio of the number of students on Team A to the number of students on Team B is 2:3. What is the ratio of money collected per student on Team A to money collected per student on Team B?
(A) 4:5
(B) 5:4
(C) 5:6
(D) 5:9
(E) 9:5
Step one: read through the entire problem, including the answer choices. It’s okay to jot down the given information on your paper, but don’t start writing equations.
Step two: identify the simple unknowns. In this step, ask yourself: what number or numbers would I most like to know? In this problem, you’d like to know the number of students on each team and the amount of money raised by each team.
Step three: choose your numbers. The numbers should fit what the problem tells you, and they should be easy to do math with. For instance, you can’t just pick any number for the number of students on Team A and the number of students on Team B. You need to pick numbers that have a 2:3 ratio, in order to match what the problem says.
Here’s what your scratch paper might look like after this step:
Team A: $50, 2 students
Team B: $60, 3 students
Step four: solve the problem, using your numbers instead of the variables. Don’t write down equations with variables! Instead, just do math with the numbers you’ve already picked.
Team A: $50 / 2 students = $25/student
Team B: $60 / 3 students = $20/student
25:20 = 5:4
The answer to this problem is 5:4. Choose (B) and move on to the next problem!
If there are variables in the answer choices, rather than relationships, you’ll need to do one extra step before picking the answer. The first four steps are exactly the same, so practice them on your own with this problem before reading further.
If a, b, c, and d are consecutive integers and a < b < c < d, what is the average (arithmetic mean) of a, b, c, and d in terms of d?
(A) d – 5/2
(B) d – 2
(C) d – 3/2
(D) d + 3/2
(E) (4d – 6)/7
Step one: Read the entire problem! You know you can use smart numbers because the answer choices are written in terms of the variable d.
Step two: The simple unknowns are the four unknown values, a, b, c, and d.
Step three: Choose some small, simple consecutive integers, like 1, 2, 3, and 4.
Step four: Solve the problem. You’ll end up with a number as your answer. The arithmetic mean of 1, 2, 3, and 4 is (1 + 2 + 3 + 4)/4, which equals 5/2.
Step five: This is the trickiest part. You know what your answer should equal: it should come out to 5/2. However, the answer choices are expressions with variables, not numbers. To finish the problem, you need to determine which of those expressions comes out to 5/2.
To do that, you have to replace the variable d with a number. Don’t replace d with 5/2! You chose a value for d earlier in the problem: d equals 4. Plug in 4 to each answer choice.
(A) 4 – 5/2 = 3/2
(B) 4 – 2 = 2
(C) 4 – 3/2 = 5/2
(D) 4 + 3/2 = 11/2
(E) (16-6)/7 = 10/7
Answer choice (C) comes out to 5/2. Since we know that the right answer to the problem is 5/2, it’s a match! (C) is the right answer.
How Can I Practice?
Using smart numbers to solve GMAT Quant problems will probably feel unnatural at first. That goes away with consistent practice. Part of what the GMAT tests is your ability to learn new approaches and unusual ways of thinking—think about how weird Data Sufficiency problems seemed when you first saw one!
The best way to practice is to consistently use smart numbers whenever you get the opportunity, even if you don’t feel comfortable with them yet. Try this exercise to really drive the concept home, as well. Open your Official Guide to the GMAT to the Problem Solving section. Skim through the problems, only looking at the answer choices. You’ll notice that most problems have numerical answer choices, but many problems have variables, fractions, percents, or ratios. Whenever you see any of those things in the answer choices, stop and read the entire problem from beginning to end. Then, try to solve it using smart numbers. Finally, take notes: did it work? Why or why not? Did you do all of the steps correctly? If you really get stuck, check out the explanations in GMAT Navigator—when a GMAT Quant problem can be solved using smart numbers, we’ll walk you through exactly how to do it. ?
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Chelsey Cooley
is a Manhattan Prep instructor based in Seattle, Washington. Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170/170 on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.