Examples of Ratio Problems on the GMAT

When studying for the GMAT, some questions will undoubtedly bring back fond memories of high school math classes, cramming for exams and wondering if that classmate you had a crush on even knew you existed (note: this may also remind you of Dawson’s Creek). Algebra and Geometry concepts evoke these feelings of nostalgia, because unless you’re an engineer or an architect (perhaps Art Vandelay?), you probably haven’t thought about the concepts in a decade or two.

However, the GMAT is not just an excuse to dust off the old high school books, some concepts you actually use in your daily life. Today I’d like to spotlight ratios. Whether cooking a good meal (3 cups of rice feed 4, but I need to feed 6) or working on your fantasy football league (Rodgers throws five touchdowns for every interception), chances are you use ratios subconsciously every day. The difference is that ratios are easy to conceptualize. Of course, this doesn’t mean that the execution isn’t tricky.

Let’s start with the notation. The GMAT can throw questions at you in three different ways. If the question wants to tell you that you need one cup of milk for every three cups of water, it could write it as “1:3”, “1/3” or “1x + 3x = total”. Without having to think about it too much, you can probably see that the first notation (1:3, read as 1 to 3) is the best one. The second notation looks exactly like a fraction, and that can lead to shenanigans. The third notation is the equation form, where x is the multiplier that will yield the proper numbers. I recommend always using the first notation, and transforming other notations into this form for consistency.

Let’s look at a simple problem to highlight the difference in notation:

In a solution the ratio of alcohol to water by volume is 1:4. The percent of alcohol is closest to:

(A)   14%

(B)   20%

(C)   25%

(D)   30%

(E)    50%

If you read the problem as ¼ ratio, you will be very tempted to pick C) 25%. However what’s really going on here is that there is one ounce (or ml or even a gill) of alcohol for every four ounces of water. This means that the percentage of alcohol is one ounce out of five total ounces. The answer is thus B) 20%.

Now that we’ve (hopefully) cleared up any misconceptions about the notation, let’s delve into how these questions are made more difficult. If we stick with the earlier Aaron Rodgers (who’s not Captain America, that’s Steve) analogy, we can compare his touchdowns, his interceptions, his fumbles, his yards gained, his games played (and possibly even his public scandals avoided). All of these numbers can be expressed as ratios of one another. How many touchdowns per game, how many fumbles per touchdown, how many yards gained per completion, and so on. Ratios don’t have to be necessarily 1:1 (see what I did there?). The exam excels at giving you multiple data points that are all in relation to one another.

Let’s look at a simple execution of a ratio question and how to solve it:

Four supporting beams (north, east, south and west) are holding up a house with weight distribution in the ratios 3:4:7:9, respectively. There is no other support for the house. If the Eastern beam is holding up 20,000 pounds, what is the total weight of the house?

(A)   80,000 pounds

(B)   92,000 pounds

(C)   115,000 pounds

(D)   320,000 pounds

(E)    460,000 pounds

If we approach this problem logically, we can see that we have all the information needed for the Eastern beam, and we can then use this information to solve for the other three beams. If the Eastern beam represents 4 units, and this translates into 20,000 pounds, then each unit must be worth (20K/4) = 5,000 pounds. If each unit is worth 5K, then the North beam is (3 x 5K) = 15,000, South is (7 x 5k) = 35,000 and the West Beam is (9 x 5K) = 45,000 pounds. Adding these four numbers together, we get 115,000 pounds, which is answer choice C.

There is an alternative solution that is slightly faster. Instead of calculating all four beams and adding them together, we can make one simple multiplication. If the Eastern beam is 20,000 pounds, that means each unit is 5K. The ratio of 3:4:7:9 has a total of (3+4+7+9) = 23 units. Each one is worth 5K, so the total is simply 23 x 5k = 115,000 pounds. Instead of doing four additions I can get there in one straightforward multiplication.

This method is slightly faster, but doesn’t provide the same level of flexibility as the previous method. Imagine if the question was “how much more weight is the Southern beam holding than the Northern beam” or “how much weight is Kanye West’s daughter holding”? (Note: Answers are 20,000 pounds and 60,000 pounds respectively). The first method provides potentially useful information, but either method is sufficient for answering the question asked.

When it comes to ratios, don’t let the notation throw you off. Become familiar with it and always transform it into a format that you’re familiar with. Also remember that the questions will never be that difficult, and that doing a little bit of math can help you confidently answer the question. Follow these simple tricks and watch the ratio of your GMAT score to the amount of time studied rise.

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Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.