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In this series we return to classic movies to learn fundamental strategies for GMAT Success.
There are two facets to each quantitative problem – (1) deciding what to do and (2) then actually doing the math. I refer to these respectively as the “diagnosis” and “surgery.”
A Good Diagnosis Avoids Unnecessary Surgery On the GMAT “diagnosis” means to read the problem, do a quick triage of what is asked and what information is given, and come up with a plan of action. “Surgery” is how I refer to the careful completion of the actual math. I use the word “surgery” in order to emphasize the fact that the math must be done with focus and with care and is not something to take for granted.
One aspect of the quantitative section is that “a good diagnosis avoids unnecessary surgery.” In this scene from the movie Doc Hollywood, the main character, played by Michael J. Fox, is about to send a kid in for open heart surgery when the wise old physician steps in and gives him a can of carbonated soda instead. Talk about avoiding unnecessary surgery!
(Note: This clip contains some coarse language).
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What this clip illustrates is the value of making sure of your diagnosis before you launch into anything too extreme. Doc Hollywood is prescribing heart surgery and the cure turns out to be a soda. When applying this principle to the GMAT you will want to go ahead and complete any simple math such as addition or easy multiplication. If the “surgery” (or math) is going to take less than 20 or 30 seconds then it is certainly worth doing and you should not really waste your time looking for an easier way. It is when the math is complicated and has lots of potential for error (like major surgery) that you want to be sure of your diagnosis.
Put It into Practice Apply this knowledge to the following problem from the Veritas Prep Statistics and Combinatorics book:
A company assigns product codes consisting of all the letters in the alphabet. How many product codes are possible if the company uses at most three letters in its codes, and all letters can be repeated in any one code?
(A) 15,600
(B) 16,226
(C) 17,576
(D) 18,278
(E) 28,572
Do you have the answer? Before you run off and start taking 26 to the power of 3, you will want to think about ways to avoid all of that unnecessary surgery.
The question says, “at most three letters” in a code and “all letters can be repeated in any one code.” The first statement means that you have multiple problems within one question and the latter statement means that this is not a permutation or combination, but it is an example of “independent selection.”
Basically, since any number can be repeated you could have a one letter code with 26 possibilities, or a two-letter code with 26 * 26 possibilities, or a three letter code with 26 * 26 * 26 possibilities. Since the questions says “at most 3 letters” one, two, and three letter codes are all valid options. You do not need to choose one, but should include all three in your answer. Calculate the number of possibilities for each option and then add them together: so 26 + 262 + 263.
Unless there is an easier way. This is a good time to look at the answer choices. You are generally looking for either answers that are spread very far apart or answers that have distinctive unit’s digits. These are often the best ways to avoid doing messy math in this situation. If the answers have large gaps you should estimate. In this case estimating is not that simple, so you should go with the unit’s digit. You will find that any power of 6 results in a unit’s digit of 6. Therefore, 26 has a unit’s digit of 6 as does 262 and 263. Therefore the unit’s digit of the answer is 8 (6 + 6 + 6 is 18 for a unit’s digit of 8). The correct answer is D.
Think Like a Doctor Doc Hollywood is an absolutely classic movie from the 1990s, and it illustrates a classic truth about the Quantitative section. If you are about to do some very complicated math, you might want to step back and make sure of your diagnosis. After all, as you are in the process of multiplying three digit numbers together, you do not want some older, wiser GMAT test-taker to give you that look of disdain and say “Nice job, Hollywood.”
David Newland has been teaching for Veritas Prep since 2006, and he won the Veritas Prep Instructor of the Year award in 2008. Students’ friends often call in asking when he will be teaching next because he really is a Veritas Prep and a GMAT rock star! Read more of his articles here.
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