The Trick Behind Percentages on the GMAT

Percentages represent one of the most underestimated question types on the GMAT quant section. Absolute numbers are helpful to give concrete information (I spent 70$ on the latest Grand Theft Auto game), but percentages give a better indication of relative amounts of time (I spend 68% of my free time playing GTA V). Based on the first, you may find that I overpaid for the video game, but based on the second statistic, I probably got a very good return on my investment.

One of the most troublesome downsides of percentage questions is that they can become confusing based on different wording. For example, if you make 50,000$ per year and your salary doubles, you now make 100,000$ per year. This represents 200% of your original salary, but only a 100% increase of your income. Thus, if you were to answer a question based on this information, the correct choice could easily be 100% or 200%. Ergo, depending on the phrasing of the question, the answer could vary between multiple different options.

The word percent actually derives from the French “Pour Cent”, which literally means “Per Hundred”. The etymology of this word is also apparent in the use of coins to denote fractions of dollars, or “cents”. While this may make sense (see what I did there), the problem is that the question will often change the number that you’re taking a percentage of, often without overtly announcing this change.

Let’s look at a typical problem that can be confusing if you go through it too quickly:

Of the 14,210 employees of the anvil factory, 2/7 are journeymen. If half of the journeymen were laid off, what percentage of the total remaining employees would be journeymen?

(A) 14.3%
(B) 16.67%
(C) 33%
(D) 28.6%
(E) 49.67%

The exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers (also because otherwise the ratio would be incorrect). Since the question is about percentages, the actual numbers will be meaningless, as only the ratio of that number versus others will be meaningful. Nonetheless, for those who are curious, each 1/7 portion represents (14,210 / 7) 2,030 employees. This in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers.

If half the journeymen were laid off, that would mean 1/7 of the total current workforce would be removed. This statistic is what leads many students to think that since half the journeymen are left, the remaining journeymen would represent half of what they used to be, which means 1/7 of the total workforce. If 1/7 of the workforce is journeymen, and 1/7 is roughly 14.3%, then answer choice A should be the right answer. In this case, though, it is merely the tempting trap answer choice.

What changed between the initial statement and the final tally? Well, you let go of 1/7 of the workforce, so the total number of workers went down. The remaining workers are still 1/7 of the initial workers, but the group has changed. The new workforce is smaller than the original group, specifically 6/7 of it because 1/7 was eliminated. The remaining workers now account for 1/7 out of 6/7 of the force, which if we multiply by 7 gives us 1 out of 6. This number as a percentage is answer choice B, 16.67%.

Using the absolute numbers we calculated before, there were 4,060 journeymen employees out of 14,210 total. If 2,030 of them are laid off, then there are 2,030 journeyman employees left, but now out of a total of (14,210-2,030) 12,180 employees. 2,030/12,180 is exactly 1/6, or 16.67%. The answer will work with either percentages or absolute numbers, but the percentage calculation will be significantly faster and applicable to any similar situation.

The underlying principle of percentages (and, on a related note, ratios) can be summed up in the brainteaser I like to ask my students: If you’re running a race and you overtake the 2nd place runner just before the end, what position do you end up in?

The correct answer is 2nd place.

Percentages, like ratios and other concepts of relative math (which isn’t how many cousins you have), depend entirely on the context. Whether 100% more of something is better than 50% more of something else depends on the context much more than the percentages quoted. As the old saying goes, 42% of statistics are meaningless, and 81% of statistics are made up on the spot. When it comes to percentages on the GMAT, the goal is to understand them enough to instinctively not fall into the traps laid out for you, like a 6th sense.

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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.