How to avoid traps on Data Sufficiency

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 Data Sufficiency question that appears to be easier than it is: Joanna bought only Rs0.15 stamps and Rs0.29 stamps. How many RS.0.15 stamps did she buy? 1) She bought Rs.4.40 worth of stamps 2) She bought an equal number of Rs.0.15 stamps and Rs.0.29 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 you call “F” the number of 15 cent stamps and “T” the number of 29 cent stamps, all you 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, you 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,you 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. You know for sure that the answer cannot be E – if you can solve for the unknowns when you are testing the statements together, you clearly have sufficiency there. And you 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. You know that you cannot purchase a fraction of a stamp, so both F and T must be integer values. That’s interesting. you also know that the total amount spent on stamps is Rs.4.40, or 440 paise, which has a units digit of 0. When you are buying 15 paise stamps, you can spend 15 paise if you buy 1 stamp, 30paise if you buy two, etc. Notice that however many you buy, the units digit must either be 5 or 0. This means that the units digit for the amount you spend on 29 paise 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 you are multiplying by 29 is if the other number ends in 5 or 0 . In other words, the number of 29 paise stamps you buy will have to be a multiple of 5 so that the amount you spend on 29-cent stamps will end in 5 or 0. Here’s the sample space of how much you could have spent on 29-cent stamps: Five stamps: 5*29 = 145 paise Ten stamps: 10*29 = 290 paise Fifteen stamps: 15* 29 = 435 paise Any more than fifteen 29-cent stamps and you are over 440, so these are the only possible options when testing the first statement. Let’s evaluate: say you buy five 29 paise stamps and spend 145 cents. That will leave you with 440 – 145 = 295 paise left for the 15 paise stamps to cover. But you can’t spend exactly 295 cents by purchasing 15 paise stamps, because 295 is not a multiple of 15. Say you buy ten 29 paise stamps, spending 290 paise. That leaves 440 – 290 = 150. Ten 15 paise stamps will get you there, so this is a possibility. Say you buy fifteen 29 paise stamps, spending 435 paise. That leaves 440 – 435 = 5. Clearly that’s not possible to cover with 15 paisestamps. Only one option works: ten 29 paise stamps and ten 15 paise stamps. Because there’s only one possibility, Statement 1 alone is sufficient, and the answer here is actually A. Takeaway: 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.