When I’m not teaching GMAT classes or writing posts for our fine blog, I am, unfortunately, writing fiction. Anyone who has taken a stab at writing fiction knows that it’s hard, and because it’s hard, it is awfully tempting to steer away from pain and follow the path of least resistance.
This tendency can manifest itself in any number of ways. Sometimes it means producing a cliché rather than straining for a more precise and original way to render a scene. More often, it means procrastinating – cleaning my desk or refreshing espn.com for the 700th time – rather than doing any writing at all. The point is that my brain is often groping for an easy way out. This is how we’re all wired; it’s a dangerous instinct, both in writing and on the GMAT.
This problem is most acute on Data Sufficiency questions. Most test-takers like to go on auto-pilot when they can, relying on simple rules and heuristics rather than proving things to themselves – if I have the slope of a line and one point on that line, I know every point on that line; if I have two linear equations and two variables I can solve for both variables, etc.
This is not in and of itself a problem, but if you find your brain shifting into path-of-least-resistance mode and thinking that you’ve identified an answer to a question within a few seconds, be very suspicious about your mode of reasoning. This is not to say that you should simply assume that you’re wrong, but rather to encourage you to try to prove that you’re right.
Here’s a classic example of a GMAT Data Sufficiency question that appears to be easier than it is:
Joanna bought only $.15 stamps and $.29 stamps. How many $.15 stamps did she buy?
1) She bought $4.40 worth of stamps
2) She bought an equal number of $.15 stamps and $.29 stamps
Here’s how the path-of-least-resistance part of my brain wants to evaluate this question. Okay, for Statement 1, there could obviously be lots of scenarios. If I call “F” the number of 15 cent stamps and “T” the number of 29 cent stamps, all I know is that .15F + .29T = 4.40. So that statement is not sufficient. Statement 2 is just telling me that F = T. Clearly no good – any number could work. And together, I have two unique linear equations and two unknowns, so I have sufficiency and the answer is C.
This line of thinking only takes a few seconds, and just as I need to fight the urge to take a break from writing to watch YouTube clips of Last Week Tonight with John Oliver because it’s part of my novel “research,” I need to fight the urge to assume that such a simple line of reasoning will definitely lead me to the correct answer to this question.
So let’s rethink this. I know for sure that the answer cannot be E – if I can solve for the unknowns when I’m testing the statements together, I clearly have sufficiency there. And I know for sure that the answer cannot be that Statement 2 alone is sufficient. If F = T, there are an infinite number of values that will work.
So, let’s go back to Statement 1. I know that I cannot purchase a fraction of a stamp, so both F and T must be integer values. That’s interesting. I also know that the total amount spent on stamps is $4.40, or 440 cents, which has a units digit of 0. When I’m buying 15-cent stamps, I can spend 15 cents if I buy 1 stamp, 30 cents if I buy two, etc.
Notice that however many I buy, the units digit must either be 5 or 0. This means that the units digit for the amount I spend on 29 cent stamps must also be 5 or 0, otherwise, there’d be no way to get the 0 units digit I get in 440. The only way to get a units digit of 5 or 0 when I’m multiplying by 29 is if the other number ends in 5 or 0 . In other words, the number of 29-cent stamps I buy will have to be a multiple of 5 so that the amount I spend on 29-cent stamps will end in 5 or 0.
Here’s the sample space of how much I could have spent on 29-cent stamps:
Five stamps: 5*29 = 145 cents
Ten stamps: 10*29 = 290 cents
Fifteen stamps: 15* 29 = 435 cents
Any more than fifteen 29-cent stamps and I ‘m over 440, so these are the only possible options when testing the first statement.
Let’s evaluate: say I buy five 29-cent stamps and spend 145 cents. That will leave me with 440 – 145 = 295 cents left for the 15-cent stamps to cover. But I can’t spend exactly 295 cents by purchasing 15-cent stamps, because 295 is not a multiple of 15.
Say I buy ten 29-cent stamps, spending 290 cents. That leaves 440 – 290 = 150. Ten 15-cent stamps will get me there, so this is a possibility.
Say I buy fifteen 29-cent stamps, spending 435 cents. That leaves 440 – 435 = 5. Clearly that’s not possible to cover with 15-cent stamps.
Only one option works: ten 29-cent stamps and ten 15-cent stamps. Because there’s only one possibility, Statement 1 alone is sufficient, and the answer here is actually A.
Takeaway: Don’t take the GMAT the way I write fiction. Following the path of least-resistance will often lead you right into the trap the question writer has set for unsuspecting test-takers. If something feels too easy on a Data Sufficiency, it probably is.
*Official Guide question courtesy of the Graduate Management Admissions Council.