As Hip Hop Month rolls along in the GMAT Tip space, we’ll pass the torch from classic artists to the future, today letting Drake take the mic.
In MBA-speak, Drake is a natural Kellogg candidate, a collaborative type who loves group projects, always appearing on tracks with other artists and bragging not just about his own success, but “now my whole team here.” So in that teamwork spirit, let’s work with Drake to help him solve his most famous math problem with some lyrics of his own:
The problem: “The square root of 69 is 8 something; I’ve been trying to work it out”
The solution: “Started from the bottom, now we here.”
On the GMAT, a problem that asks you for the square root of a not-that-common square (you have to have the squares memorized up to about 15 and you should know that 25^2 is 625, too) is almost always going to be an exercise in “starting from the bottom,” using the answer choices to help guide your work. The GMAT doesn’t care if you can calculate the square root of 69, but it does care about whether you can leverage assets like answer choices to help you solve the problem. So on a problem like Drake’s, answer choices might look like:
(A) Between 6 and 7
(B) Between 7 and 8
(C) Between 8 and 9
(D) Between 9 and 10
(E) Between 10 and 11
And in that case, starting from the bottom – looking at the answer choices before you begin your work – can tell you two things:
1) You don’t need an exact number; an estimate will suffice.
2) They’re giving you the numbers to use as an estimate; if you start in the middle of the range (using 8 and 9), you can determine whether you need bigger or smaller numbers.
So if you try 8^2 to give yourself a range of numbers, you’ll see that the square root of 69 is going to be bigger than 8, since 8^2 is 64. So then try the next highest integer, 9, and when you see that 9^2 is 81, bigger than 69, you’ve bracketed in the range at between 8 and 9 and you don’t need to do any more work. When math looks like it could be labor-intensive, the answer choices often show you that you don’t have to do it all!
Even if the problem were a bit tougher, and gave exact numbers like:
You could again lighten the load by picking an easier-to-calculate number in between, like 8.5. That’s not the easiest math in the world, but multiplying by 5s is typically fairly quick and you’d see that the number has to be less than 8.5 (since 8.5-squared is 72.25).
So the lesson is this – on most Problem Solving and Sentence Correction questions, it pays to “start at the bottom” so to speak, at least taking a quick glance at the answer choices to see if anything jumps out to help you guide your work on the problem. For Problem Solving, some of the prime candidates are:
- If the units digits of the answers are all different, you can shortcut the multiplication
- If one variable from the problem (say the problem has x, y, and z) is missing in the answers (say they only have x and z), you’ll want to start working to eliminate that missing variable
- If the answer choices contain telltale signs of a certain shape or relationship (the square root of 3 usually comes from a 30-60-90 or equilateral triangle; pi usually comes from circles), your job is to find and leverage that shape
- If the answer choices include fractions, you can use the factors in the numerator and denominator to guide your math (for example, if three of the choices have a denominator of 3 and two have a denominator of 6, part of your work will include the question “will the denominator be even?”)
On Sentence Correction, pay attention to the first and last words (or phrases) of the answer choices for obvious differences. You may see:
- Two use a singular pronoun (its) and three use a plural (their) – this means that as you read the sentence you’re looking to find the noun that the pronoun refers to
- The answer choices use different tenses of the same verb (are vs. were vs. have been) – this means that your job is to pay attention to the timeline in the sentence to see which verb tenses are consistent with the logical sequence of events
- Two use “that of (noun)” and three just use the noun – this means that there’s a comparison going on, and you need to determine whether you’re comparing the possessions (the GDP of Canada vs. that of the UK) or the nouns themselves
Naturally, there are many, many more examples of clues that the answer choices can leave for you, so the true lesson is as simple as Drake’s lyrics. On Problem Solving and Sentence Correction problems, start (briefly) from the bottom to see if there’s anything you can glean from a quick peek at the answers that will help you more quickly get “here”, to the right answer.
By Brian Galvin