Today’s GMAT article comes from Manhattan Review Asia, a provider of GMAT private tutoring in Hong Kong, Kuala Lumpur, Manila, and Singapore, among others. In this article, they reveal Manhattan Review’s best 5 strategies how to tackle GMAT Problem Solving questions. In fact, the article is so detailed that we had to split it into two parts. If you have missed the first part of this post, you can find it here.

## 4. Skipping the Algebra

The most effective way to solve problems quickly is to make up numbers. Problems involving ratios and percentages are very susceptible to solution by this method. You can of course solve such problems using algebra, but it takes so much longer.

Consider a question of the form “There are three times as many third-graders as fourth-graders at a picnic. There are also twice as many first-graders as there are second-graders. If there are four times as many third-graders as there are second-graders, what percentage of the total number of children at the picnic comprises fourth-graders?” This is a classic GMAT-style question. The quickest way to solve it is to pick arbitrary but simple numbers. Let’s assume that there are 20 fourth-graders at the picnic. That means that there must be 60 third-graders. That in turn must mean that there are 15 second-graders. Which means that there are 30 first-graders there.

Under these conditions, the total number of students at the picnic would be 30 + 15 + 60 + 20 = 125. The percentage that is comprised of fourth-graders would be 20/125 x 100 = 16%. Now, let’s apply this method to a GMAT problem. It comes from the Manhattan Review Study Companion:

Admission to a certain ballet school is very competitive. 3/8 of all applicants are male. 3/4 of all applicants are rejected in the first round including 2/3 of all male applicants. What fraction of applicants remaining after the first round are male?

(A) 1/32

(B) 1/4

(C) 1/2

(D) 3/4

(E) 8/9

Let’s pick our easy numbers. Let’s say that there are 80 applicants. 3/8, or 30, are male; 5/8, or 50, are female. 3/4 of all applicants are rejected. 3/4 of 80 = 60. That 60 includes 2/3 of all of the male applicants. 2/3 of 30 = 20. The total number of applicants who remain is 80 – 60 = 20. The total number of male applicants who remain is 30 – 20 =10. So what fraction of the applicants remaining after the first round is male? The answer is 10/20 = 1/2. The answer is (C).

A question that might have taken us four minutes to solve using algebra can be knocked off in less than 30 seconds.

## 5. Making Algebra work for you

There are of course times when algebra is unavoidable. If the question isn’t asking about ratios or percentages but is instead seeking actual numbers, then we have no choice but to set up equations. It is very important to remember that you can’t keep applying the same method to every problem. Picking arbitrary numbers doesn’t always work. Let’s take a look at a question that isn’t susceptible to solution by substitution. Again, it comes from the Manhattan Review Math Study Companion:

The population of Country S is 10 million people less than the population of Country J. If in 5 years, Country J has twice as many people as Country S, how many people will live in Country S in three years given that each country has a constant population growth of 0.5 million people per year?

(A) 6

(B) 7.5

(C) 9

(D) 10.5

(E) 12

The question, like many GMAT questions, is confusing. The information is presented in a not especially helpful way. Let’s set out the issues in as lucid way as possible. Don’t clutter up your calculations with “x”s and “y”s. Since it’s the population of Country S that we’re after, let’s call it S. That means that the population country J at the moment is S + 10. Since the population of both countries grows at the rate of ½ a million a year, then in five years’ the population of country S will be S + 5/2. The population of Country J will be S + 10 + 5/2. At this point the population of Country J will be twice the population of Country S.

Thus we have our equation:

S + 10 + 5/2 = 2 (S + 5/2)

S + 10 + 5/2 = 2S + 5

S = 5 + 5/2 = 7 ½

It is very tempting at this stage to look at the answer choices and to plump for (B). However, that’s a trap. The question isn’t asking what is the population of Country S. It’s asking what the population of Country S will be in three years’ time. Therefore, we will need to add 3 x 1/2 = 3/2 to 7 1/2. The answer is 9 million or (C).

The equations are straightforward. The difficulty of the problem was translating the information into that straightforward equation.

Best of luck on your GMAT! If you want to know more about the GMAT Preparation options from Manhattan Review, please attend a free interactive GMAT webinar that will feature many suggestions and tricks how to prepare for the test. Please also be sure to check out the free Manhattan Review GMAT Sentence Correction Guide.