Executive Assessment: Fast Math for Faster Solutions – Part 5
Welcome to the fifth installment of Fast Math for the EA! If you’re just joining us now, head back to the first part and work your way back here.
So far, we’ve done problems that are found in the Quant section of the exam. Today, we’re going to try an Integrated Reasoning (IR) problem. IR problems can be quant-focused, verbal-focused, or a mix of the two. Since this series focuses on Fast Math, we’ll be looking at quant-focused IR.
“Organization A currently has 1,050 members. Organization B currently has 1,550 members. The number of members of Organization A and the number of members of Organization B are increasing annually, each at its own constant rate. Analysts project that if each of these organizations maintains its constant annual rate of membership increase, five years from now they will for the first time have the same number of members, and in subsequent years Organization A will have more members than Organization B.
“In the table below, identify a rate of increase, in members per year, for Organization A and a rate of increase, in members per year, for Organization B that together are consistent with the analysts’ projection. Make only one selection in each column.
That’s a lot of information. What’s the best way to process it all and figure out a plan to solve?
Your First Glance tells you that this is a 2-Part problem (one of the 4 question types given in the IR section). That glance also indicates that this is a quant-focused problem (see the numbers in the answer choices?).
Quant-focused 2-Parts can come in one of two overall “flavors”: Independent or connected. Let’s talk about what that means.
2-Part: Independent or Connected?
All 2-parts, as the name implies, will ask you to solve two parts of a problem. You’ll always see a table like the one above and you’ll have to select one answer in the first column and one answer in the second column.
Sometimes, the work you need to do to find the first answer is independent of the work you need to do to find the second answer. In this case, you’re basically answering two different questions (though you are working from the same base of information).
Other times, the answers will be co-dependent: It’s impossible to solve for just one by itself. You literally have to solve for the two answers at the same time.
Glance back at this problem. Is this one independent or connected?
The problem asks you to find two answers that together are consistent with the information in the problem. In other words, this is a connected problem.
Okay, we’re up to the Read and Jot stage. Here’s what I jotted down.
You might notice certain things that I did not write down. I didn’t write down that each one is growing at a constant rate. For most of these types of problems, the default position is to have something grow at a constant rate. If a problem told me something was growing but not at a constant rate, I would write that down.
I also haven’t written down anything from the question stem yet—I need to Reflect on that first.
The word together told me that this was a connected problem. When this is the case, I’m usually going to go to the answer choices and Work Backwards to find the pair that works together. Is that also going to be the case this time?
Let’s see. They asked me to find the rate of increase in members per year for each organization. Oh, that’s weird—I was expecting those to be percentages (e.g., membership is increasing by 10% per year, and so on). But no…these aren’t percentages. They literally mean the number of members—it’s growing by 10 members a year, etc.
Okay. Actually, that’s good. I thought I was going to have to calculate the percent increase year over year for 5 years. That’s really annoying even with a calculator. But they’re just straight up giving me the possible # of additional members…so, yes, I’m just going to work straight from the answers to find the pair that will work.
Also note that there are 6 answers (which is typical for 2-Part questions); this could take a while. As I try the first one, I’m going to be looking for opportunities to streamline this process.
Anything else to figure out? Or are we ready to solve?
Organization A is smaller than Organization B now, but it’s going to catch up to B in 5 years. Therefore, A has to be increasing at a faster rate. The rate of increase for B, therefore, has to be a smaller number than the rate of increase for A.
Let’s start by assuming B has the slowest rate of +10 per year. Where will B be in 5 years?
1 yr: 1,560
2 yr: 1,570
3 yr: 1,580
4 yr: 1,590
5 yr: 1,600
Okay, now A is currently at 1,050 and it has to catch up to B—so it would have to get to 1,600. That’s a difference of:
1,600 – 1,050 = 550
Per year = 550 / 5 = 110
(Since this is IR, you can pull up your calculator to do that last bit of math. Or you can use your Fast Math principles to divide by 5! Move the decimal over, so 550 becomes 55, and double that number, so 55 becomes 110.)
So A would have to grow by 110 a year to hit 1,600 in year 5. But 110 isn’t in the answer choices, so B doesn’t equal 10.
Before you try the next one, reflect on the process so far. Can you streamline?
We don’t actually care what the numbers are each year for years 1 through 4; we only need year 5. So how can we go straight for the year-5 value?
Take the rate of increase (in our first case, that was 10) and multiply by 5 (so that would be 50 for that first case). Then, add that to the starting point: 1,550 + 50 = 1,600.
Do the same for the next possible rate of increase, 30:
(30)(5) = 150
1,550 + 150 = 1,700
Now find what A would have to be.
1,700 – 1,050 = 650
650 / 5 = 130
Check it out! 130 is in the answers, so this is the correct pairing.
The correct answer is 130 for the first column and 30 for the second column.
One last note: Careful not to mix those two up! If you put 30 and 130 (in that order), you wouldn’t get credit for this problem.
Join me next time, for another installment in this series.
Key Takeaways for EA Fast Math:
(1) Integrated Reasoning 2-Part problems can be independent or connected. When they’re connected, you’re probably going to Work Backwards from the answers to solve.
(2) When working backwards, still look for opportunities to use Fast Math or otherwise streamline your math! Because you’ll probably have to try multiple answers, pause briefly after your first try to see whether you can streamline your process at all.
(3) Turn that knowledge into Know the Code flash cards:
* Executive Assessment questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.