Greetings, and Happy St. Patrick’s Day weekend, readers! As a young professional, you’re most likely reading this on your smartphone while waiting in line for a pub crawl or on your laptop while you recuperate from one. And in either case, you could probably stand to benefit from one of the greatest things about Paddy’s Day: McDonald’s Shamrock Shakes. Only available for one month per year, the much-anticipated frozen treats enjoy a cult-like following (and blend perfectly with the Filet o’ Fish specials on Lenten Fridays), tweaking the classic milkshake format with a minty flavor and a seasonal green hue. Not only are these shakes among the most delicious features of spring, they can also teach you how the GMAT writes its questions. Appetized? Here’s how:
When you really break it down, the formula for Shamrock Shakes is as standard to McDonald’s as anything else; it’s a vanilla shake with a dash of mint flavor and, for its classic green color, the food coloring additives yellow 5 and blue 1. That’s it – these Shamrock Shakes that make you salivate come January waiting for their release in March are the exact same milkshakes you can order year-round, with the smallest of twists designed to make them seem so seasonally unique and delicious. And this is one of many reasons why McDonald’s, the greatest marketing organization on earth, is a lot like the GMAT, the test that can help you get into the greatest marketing MBA programs on earth. They know how to make those tiny tweaks that make massive differences, at least in perception to the end consumer.
The GMAT will do all it can to Shamrock shake your confidence and your score, employing minor tweaks to those common themes that you’ve studied, in an effort to make those routine questions that you can do in your sleep seem like uniquely-impossible challenges. And it’s in your ability to notice and follow those tiny tweaks that you can prove your worth as a McDonald’s level brand manager or CEO. Consider a topic like probability:
Browse the forums here at Beat The GMAT or talk to a handful of GMAT students and you’ll likely come away with the idea that probability is one of the “harder” topics covered on the GMAT. But that’s not necessarily the case, just as Shamrock Shakes aren’t necessarily “unique” or special milkshakes. Like most (if not all) topics on the GMAT, probability is just a way to take something that you inherently know and tweak it just enough to make it look difficult, just as a dash of yellow-5 and blue-1 will make you feel like your milkshake is enough to bring all the boys to the yard or all the snakes away from Ireland. You know that:
1) The probability of getting “heads” on a flip of a coin is .
Why? Because there are two outcomes on a coin flip – heads or tails – and one of them gets you what you want. So one out of two outcomes is favorable, and therefore there is a one-out-of-two () chance that you’ll get what you want.
Similarly, you likely know that:
2) The probability of getting “heads” twice in a row on two flips of a coin is .
Why? You may well know that you multiply , but there’s a pretty reasonable explanation for that. Now there are 4 things that can happen: HH, HT, TH, and TT. And, still, only one of those gets you what you want: HH. So one out of four outcomes gets you what you want, and the probability is then .
Perhaps most importantly, you should recognize that the denominator reflects the total number of possible outcomes, and you multiplied because, for each outcome of the first flip, there were going to be two more outcomes for the second.
If you’re following thus far, you should feel pretty confident about probability on the GMAT. You know how to find the probability of a single event, and you know how to find the probability of a sequence of events. The rest of what’s tested on the GMAT comes down mainly to tweaks on those themes. Say that the question asked for:
3) What is the probability of getting one heads and one tails on two flips of a coin?
Here they’ve changed the game a bit on you. Now there are multiple sequences that give you the desired outcome: Heads, Tails and Tails, Heads. So now the numerator is , and the denominator is still 4, so the answer is out of , or which reduces to a probability that you’ll end up with one of each.
If you feel comfortable with that, you may even be able to predict where the GMAT will go next. Two fairly natural tweaks are as follows:
4) When drawing from a jar of five green and five red marbles, what is the probability of drawing one of each color on two consecutive draws, without replacement?
Here we have a new twist – the denominator is going to be different on the second draw, because we’re taking one marble out of the jar and not putting it back. This means that the odds change for the second draw, and we need to reflect that in our math. Again, there are two ways to get what we want here: Red, then Green; and Green, then Red. So we need to calculate the probabilities of both:
Red, then Green. Well, on the first draw there are red marbles out of marbles total, so there’s a probability. But for the second, we’re saying that we took a red marble out of circulation, so there are only red marbles and green marbles left, out of a total of marbles remaining. So the probability of Red, then Green is 5 red / 10 total on the first draw, and 5 green / 9 total on the second draw, for a total probability of that we get the sequence Red, then Green.
Green, then Red. The math here will be similar to the above. There is a chance of drawing green on the first draw, with then all 5 red marbles left out of a total of 9 on the second, for a probability of x = probability of Green, then Red.
So, there is a probability of drawing one of each red and green.
Most importantly here, notice the tweaks – the probability of the second draw was different from that of the first because we removed an item without replacement, and that made for a unique twist on the coin flip discussion above.
1) On five consecutive coin flips, what is the probability of getting at least one heads and one tails?
Here, there may simply be too many outcomes to want to calculate by hand as we had done in previous coin flip examples. possible outcomes, and that’s a lot of work to do. Especially when you consider that HHHHT, TTTTH, HTHTH, THTHT, etc. are all outcomes that satisfy what we want…there are just too many to reliably draw out without accidentally missing one or two. It would be much easier if the question asked something like “probability of all heads” or “probability of all tails”. Which, not coincidentally, is how we’ll best solve this one. If the probability is going to be overwhelmingly in favor of our outcome, it will be easier to calculate the much-smaller number of outcomes that DON’T give us what we want. How many ways w ill we NOT get one of each?
Well, only if we get ALL heads or ALL tails. Each other outcome includes one of each. And we know that there is only one way to get all heads, and only one way to get all tails (either HHHHH or TTTTT). So out of outcomes does not give us the desired outcome, meaning that the other do. Accordingly, the answer is which reduces to .
Here, the tweak is that the test presented the inverse to the problem we wanted to solve (only one or two outcomes that satisfy the requirements) and instead made the problem look incredibly involved. But by recognizing that tweak, we could break the problem down to what we already know how to do well.
Naturally, this doesn’t fully summarize all the different tweaks that the GMAT could employ, but you can anticipate most of them just by adding your own variations to these. What if the two-sided coins were six-sided dice? What if the “at least one of each” problem was with the marbles in which each probability would change as we removed items?
What’s most important to recognize here is that difficult GMAT problems are often a lot like Shamrock Shakes – their genius is just a slight variation on what you’ve commonly come to accept as same old, same old, but that little tweak makes all the difference in the world.