The other day, while working with a tutoring student, I was enumerating the virtues of various test-taking strategies when the student sheepishly interrupted my eloquent paean to picking numbers. She’d read somewhere that these strategies were fine for easy to moderate questions, but that for the toughest questions, you just had to bear down and solve the problem formally. Clearly, she is not a regular reader of our fine blog.
As luck would have it, on her previous practice exam she’d received the following problem, which both illustrates the value of picking numbers and demonstrates why this approach works so well.
A total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 20 percent of the migrating geese were male, what was the ratio of the migration rate for the male geese to the migration rate for the female geese?
[Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number of geese of that sex)]
This is a perfect opportunity to break out two of my favorite GMAT tools: picking numbers and making charts. So, let’s say there are 100 geese in our population. That means that if 30% are male, we’ll have 30 male geese and 70 females geese, giving us the following chart:
Now, let’s say 10 geese were migrating. That means that 90 were not migrating. Moreover, if 20 percent of the migrating geese were male, we know that we’ll have 2 migrating males and 8 migrating females, giving us the following:
(Note that if we wanted to, we could fill out the rest of the chart, but there’s no reason to, especially when we’re trying to save as much time as possible.)
Our migration rate for the male geese is 2/30 or 1/15. Our migration rate for the female geese is 8/70 or 4/35. Ultimately, we want the ratio of the male migration rate (1/15) to the female migration rate (4/35), so we need to simplify (1/15)/(4/35), or (1*35)/(15*4) = 35/60 = 7/12. And we’re done – B is our answer.
My student was skeptical. How did we know that 10 geese were migrating? What if 20 geese were migrating? Or 50? Shouldn’t that change the result? This is the beauty of picking numbers – it doesn’t matter what number we pick (so long as we don’t end up with an illogical scenario in which, say, the number of migrating male geese is greater than the number of total male geese). To see why, watch what happens when we do this algebraically:
Say that we have a total of “t” geese. If 30% are male, we’ll have 0.30t male geese and 0.70t females geese. Now, let’s call the migrating geese “m.” If 20% are male, we’ll have 0.20m migrating males and 0.80m migrating females. Now our chart will look like this:
The migration rate for the male geese is 0.20m/0.30t or 2m/3t. The migration rate for the female geese is 0.80m/0.70t or 8m/7t. We want the ratio of the male migration rate (2m/3t) to the female migration rate (8m/7t), so we need to simplify (2m/3t)/(8m/7t) = (2m*7t)/(3t * 8m) = 14mt/24mt = 7mt/12mt = 7/12. It’s clear now why the numbers we picked for m and t don’t matter – they cancel out in the end.
Takeaway: We cannot say this enough: the GMAT is not testing your ability to do formal algebra. It’s testing your ability to make good decisions in a stressful environment. So your goal, when preparing for this test, isn’t to become a virtuoso mathematician, even for the toughest questions. It’s to practice the kind of simple creative thinking that will get you to your answer with the smallest investment of your time.