How to not waste time while solving quants

Let’s do an experiment. Grab a piece of paper, a pen, and a stopwatch (or use the stopwatch function on your mobile device). When you’re ready, click “start” on the stopwatch and begin the following Problem Solving problem… Solution A contains 20% alcohol by volume, and Solution B contains 50% alcohol by volume. If the two solutions are combined, the resulting mixture of A and B contains 32% alcohol by volume. What percent of the total volume of the mixture is Solution A? (A) 35% (B) 40% (C) 50% (D) 60% Ok, write down the answer you got, and how much time it took you. At what point did you start writing on your paper? 5 seconds into the problem? 10? 30? How long did you take on the problem overall? Believe it or not, there is probably an inverse correlation between those two answers. Students who dive in and start writing equations right away will often spend 2:30 to 3:30 on a question like this – generally much longer than students who take their time before writing things down. They’re also much more likely to get the question wrong! Savvy test takers don’t dive in and start solving right away. They know that slowing down at first (even though it seems counter-intuitive) can improve both timing and accuracy. The savvy way to approach Problem Solving questions is this: Read the entire problem, pen down. It’s not Reading Comprehension, so you don’t need to take notes! If you’re writing while you’re reading, you’re much more likely to miss key pieces of information. Think about the concept that’s being tested and what information the problem is giving you. Here’s what you should be thinking while reading the problem above: “Okay, this is a weighted average problem – we’re mixing 2 things together. They’re each different amounts of alcohol, and then we’re given a total.” Define what the question is asking for. Again, before writing equations down, just define the question. Is it asking us for a value, a sum, a difference, a proportion, a variable “in terms of” another variable, etc.? This is the best way to ensure that you don’t accidentally solve for the wrong thing! “The question is asking me about A as a percentage of the total of A and B.They’ll include a trap if you accidentally solve for B!” Scan the answers & try to eliminate. Before picking up the pen, do a common sense test first! This isn’t high school, where you have to show all of your work before picking an answer. Think of the answers as part of the problem itself! Scanning the answers first can give you powerful clues for how to solve a PS problem. For example, if a geometry problem featured √3 in some of the answer choices, that’s your clue to think about 30:60:90 right triangles. If a ratio problem featured some ratios that were greater than 1 (e.g. 3:2) and some that were less than 1 (2:3), that’s your clue to assess which portion should be greater. Some of the answer choices are less than 50%, one is 50%, and the others are greater than 50%. If you can just figure out whether you have more A or more B in the mixture, you can narrow it down.” “Since the 32% in the overall mixture is closer to A’s 20% than B’s 50%, that means that A must make up more of the overall mixture – in other words, more than 50%. I can eliminate (A), (B), and (C).” Look out for Traps As mentioned before, the CAT loves to set traps for us. If you become aware of those traps, you can narrow down answer choices easily. Here are some common traps to watch out for: Numbers in the Problem – these are rarely right answers. The CAT imagines that if a student didn’t know what to do, she would just say, “um, that number looks familiar. I guess I’ll pick it.” Don’t do that! We could eliminate (A) and (C) (if we hadn’t already) since they’re in the problem. One-Move Answers – similar to the above. If you can get to one of the answers just by performing one operation (addition, subtraction, multiplication, division) to 2 of the numbers in the problem, that’s almost certainly a trap. 50 + 20 = 70, so (E) is almost certainly a trap answer. “Evil Twins” – if we expect that the CAT is trying to trick us into answering the wrong question (for example, solving for B instead of A here), we should look for answers that form a pair. We know that the percentage of A + the percentage of B will add to 100%. So, look for 2 answers that add to 100: only (B) and (D) in this case. Since we know A has to be more than half of the total, that means that (B) is probably an “evil twin” trap! If we eliminate all of the likely trap answers, that just leaves us with (D). Be Strategic In a situation like this, the best strategic move would be to pick (D) and move on. It’s a bad idea to get bogged down in a lot of algebra just to prove what you probably already know to be true. The savvy test-taker would say “90% sure of my answer in 40 seconds is better than 100% sure of my answer in 3 minutes.” It’s an uncomfortable feeling not to know for sure, but the AT Cis a time-constrained game! You don’t have time to be 100% sure of every answer. If this question were different, and you weren’t able to eliminate all of the other answer choices, you would want to make a strategic decision about which approach would work best. Don’t just dive into doing algebra! Remember that there are other strategies that can often be faster: picking smart numbers, working backwards from answer choices, estimating, etc. On this problem, if we wanted to solve, we could do a combination of strategies. Since we don’t have any concrete amounts given, we can pick our own numbers. Let’s say that the total mixture is 100 liters. We could also work backwards from the answer choices, based on that 100L total. Since we suspect that the answer is (D), let’s then say A = 60 liters. The amount of alcohol in A would be 20% of 60, so 12L. If A is 60L, then B must be 40L. 50% of 40L would be 20L of alcohol. Thus the total amount of alcohol is 12 + 20 = 32 liters of alcohol out of 100 à 32%. That works! So (D) must be the right answer. Saving time on PS. If you did long or complicated algebra on this question, you probably took well over 2 minutes to solve. It’s also far more likely that you got the answer wrong! Putting the pen down and thinking through the problem in the way we outlined above will improve both your timing and your accuracy. The next time you’re doing a set of PS problems, write this on a post-it note and keep it next to you as you’re working: Read the entire problem, pen down Define what the question is asking for Scan answers & try to eliminate Look out for traps Be strategic (either in solving, or in guessing & moving on)