This week we have something special for our readers.
Whether you’ve seen us in class, in a free event, on this blog, or elsewhere, Kaplan always presents a unified front, as though we agree on everything. In fact, the smart, opinionated people who work for Kaplan disagree about lots of things, and today we’re offering a glimpse of our intellectual disputes.
Kaplan’s GRE bloggers Boris and Teresa take to their chairs to debate a common topic: does a GRE calculator make the test easier, or harder? Hear their arguments, pro and con, in the video below!
As always, let us know what you think in the comments below!
Knowing how to break a number apart into its factors is a useful skill that will serve you well on the GRE. However, sometimes you’re better served by not actually taking the time to determine what a number’s specific factors are. When is this a more useful approach? Take this Quantitative Comparison, for example:
We’re being asked to compare the number of non-prime, positive integers greater than 1 that are factors of Q, to 24. Do we care about what the actual factors are? Not at all. We could pick values for a, b, and c, and see how many factors of Q we can get. However, there’s a quick trick that will save us time and ensure that we don’t accidentally miss any factors.
If we only care about finding the number of factors that a given number has, then all we need to do is look at the exponents of its prime factors. In this case, we know that a, b, and c are prime, so we don’t need to regroup or simplify them at all.
All we do is add 1 to each of the exponents, and multiply the results. The exponents on a, b, and c are 2, 3, and 1, respectively. If we add 1 to each of these, we’ll get 3, 4, and 2. When we take the product, we get 24.
So can we compare this value of 24 to the value in Quantity B and move on? Not quite – remember, we specifically want to compare the non-prime factors that are greater than 1. Well, let’s figure out how many of the factors do not fit into that category. 1 certainly does, and the only primes that go into Q were given to us in the question stem: a, b, and c. So out of the 24 total factors of Q, 4 of them don’t fall into the “prime and greater than 1” category. This leaves 20 total factors, which means that our two quantities are in fact equal.
To recap the steps for finding the total number of factors of a given integer:
1) Break the integer apart into its prime factors, written with exponents (eg a3b2c).
2) Add 1 to each of the exponents.
3) Multiply the resulting terms.
Simple, yet effective – that’s my favorite kind of math trick! What are your favorite math tricks? Let us know in the comments!
As teachers, my colleagues and I spend a lot of time discussing the importance of study plans with our students – specifically, how do you continue working once you’ve completed the class sessions and the accompanying assignments? The best study plan for you will vary depending on the specific topics on which you need to improve, but we do have a basic template that you can use to plan out your studies into two-week cycles:
- Start every two week cycle with a full-length MST, to gauge your progress
- Spend the first three days after the test reviewing the answers and explanations to every problem, and doing the recommended assignments in the Smart Report. So doing the test, review, and recommended assignments can account for four days’ worth of work in each two-week cycle.
- Then spend the next two days reviewing anything else that you know you need to work on – it could be particular topics or question types, or it could be using Quiz Bank quizzes to work on pacing. This piece will change every cycle, which is why I’m being deliberately vague.
- Take day seven off – you’d take rest days if you were training for a marathon, and this is no different.
- For the five out of the next six days (the first six days of week 2) you can organize your studying by topic or question-type – Monday could be algebra day, Tuesday reading comp day, etc. Spend your time just building a 6-8-question quizzes in Quiz Bank and reviewing them thoroughly, and reviewing any book material or Lessons on Demand to review the content as necessary.
- Allot one day out of this six-day span to going back through the previous MST, to see if you remember how to solve the questions that you looked through on that test – it can be very easy to look at a problem a week after you did it and forget how to solve it. Reviewing the problems twice will help ensure that you’re remembering approaches that will help you on the next test.
- Take day seven of week 2 off, then begin the cycle again with the next MST!
Simple but effective – lather, rinse, and repeat your way to GRE success. Do you have any questions about setting up study plans? Do you have trouble sticking to the plans that you’ve set? Let us know in the comments!
I hear this from a lot of you. Unfortunately, as I explained recently, having more time on the GRE wouldn’t actually help you get a higher score, since the GRE is a scaled test. So let’s leave the complaining to our competition, shall we? Instead of moaning about the clock, strive be as awesome as you can at solving problems. If you’re great, you’ll also be fast. Here’s a quantitative comparison that’s pretty simple, but also a nice illustratration of the fact that speed isn’t something that comes independently of problem solving skill.
This problem, like several I’ve been looking at recently, comes from our GRE Bootcamp event:
Quantity A: The sum of all integers from 9 to 29, inclusive
Quantity B: The sum of all integers from 12 to 30, inclusive
At a glance, the “math” way to solve this problem is time-consuming but direct: add up the sums in both columns, then compare. Since there’s an on-screen calculator on the GRE, some of your competition will solve the problem this way. And boy does it take a long time.
Let me be very clear: directly totaling both columns isn’t just a slow way to solve the problem. It’s a BAD way. Someone who solves the problem in this head-on, brute force fashion, then says to themselves, “I’m fine with the problems, it’s the timing that kills me,” is being dishonest with themselves. They are not ”fine with the problems.” They are very much unfine!
Instead, when you have to compare two quantities, start by eliminating what they have in common. If a quantity appears in both columns, then it isn’t helping either one to be bigger than the other.
Here, both columns include the range of numbers 12-29. Thus, totaling that range would be a waste of time. Ignore it and look instead at what’s different:
Quantity A: The sum of all integers from 9 to 11, inclusive
Quantity B: The of all integers from … never mind, it’s just 30!
And since 9 + 10 + 11 clearly equals 30, you can click choice (C) — “The two quantities are equal” — in under 10 seconds and score the point. That’s the beauty of the GRE: if you’re awesome, speed comes for free. Practice will get you there!
Which of the following is equivalent to (√3 + 1) / (√3 – 1)?
(A) 3 – √3
(B) 2√3 – 2
(D) 2 + √3
(E) 4 + 2√3
Several of us instructors looked at the problem, and without even glancing at the answer choices, half of us said “Whichever choice is equal to 2.” But when we actually read the answer choices, we noticed that there wasn’t one that matched our prediction.
Where did we go wrong? It was hubris. We’ve all been teaching for long enough that we know the common math tricks inside and out – in this case, as soon as we saw (√3 + 1) and (√3 – 1), we noticed that they looked like the terms in the common quadratic equation (a + b)*(a – b), and assumed that we were supposed to multiply the terms together. In that case, the result would be 3 – 1, which equals 2. Of course, the problem asks us to divide the terms, not multiply them, but we’d read too quickly and made a fatal mistake. We were able to fix it, but only after we had 1) realized that no choice matched our result, and 2) gone back and reread the question. That’s a lot of time wasted, on a problem that – if read correctly on the first pass – can be solved with a couple of very straightforward calculations.
If it was so easy for a group of people who have been teaching the GRE for decades (albeit a group who was half-distracted with work) to read too quickly, just think how easy it is for the average test-taker to fall into a similar trap. So learn from our mistake: Know every shortcut and approach that you can possibly learn, but do not ever, under any circumstances, let that be a substitute for reading carefully and identifying exactly what a question is asking you to do.
What traps do you commonly fall into in your GRE practice? And what answer did you get to this quant problem? Let us know in the comments!