Executive Assessment: Quant Strategies for Faster Solutions – Part 3

by on November 12th, 2017

math2Welcome to the third installment of Quant Strategies for the EA!

If you’re just joining us now, you might want to go back to the first part and work your way back here.

Today, we’re going to tackle a quant-focused Graph question from the Integrated Reasoning (IR) section of the EA (this one is labeled #3 in the Graph set on the EA website, as of November 2017):

“The graph models the hypothetical mass, in kilograms, of a Tyrannosaurus rex up to 30 years of age. Points A, B, and C represent the masses for a Tyrannosaurus rex at ages 12, 16, and 20, respectively, according to the model.

“From each item in the drop-down menu, select the option that creates the most accurate statement based on the information provided.

“For integer values of the age from 12 to 30, the average (arithmetic mean) mass falls approximately between _______________ kilograms.

“The percent change in the mass from age 12 to age 16 is approximately _______________ the percent change in the mass from age 16 to age 20.”

Answer options for blank 1:

“2,000 and 3,000

“3,000 and 4,000

“4,000 and 5,000”

Answer options for blank 2:

“equal to

“2 times

“3 times”

It was kind of annoying to have to look down below to see the answer options, wasn’t it? The good news is that it’s not quite that annoying on the real test—on the real thing, each blank will have a drop-down menu that you can click to see the answer options.

So why didn’t I put the answer options just below each blank? Because you do have to remember to click—and I don’t want you to even think about starting to work on a Graph question before looking at the answer options.

I made it a little annoying / cumbersome here, so that you would think to yourself, “Wait, where are the answers?” Always click. Always check. Then, decide how you would like to solve.

Let’s do this!

Glance: It’s a line graph. Only 3 data points, interesting. X-axis is age in years and y-axis is mass in kilograms.

Read & Jot: The three points represent three specific ages. Jot that down. That’s pretty much it to start.

Review the statements and reflect.

Statement 1 asks for the average mass from age 12 to 30. Glance at the graph. Point A is age 12, and the very end of the graph is age 30. Okay.

Technically, to find the average, I’d have to find the sum of each of those data points and divide by the number of points. But there are too many data points—even with a calculator, that would take way too long. So there must be some other way to do this. What?

The clue is in the answers! Each answer represents a wide swath of the y-axis, so we don’t actually have to calculate precisely; we can estimate.

And check it out! The statement actually uses the word approximately. When they ask for an approximate answer, do check the answer choices to make sure they’re sufficiently spread out—but, if they are, then trust the test-writers. Estimate!

Statement 2 is confusing—I had to read it twice. I did notice something on my first readthrough, though: the word approximately is there again. And look at how spread out the answers are! 1x, 2x, 3x—we can definitely estimate here. :)

I’m going to go to the first statement now and figure that out. Then I’ll reflect on that second statement again.

“For integer values of the age from 12 to 30, the average (arithmetic mean) mass falls approximately between _______________ kilograms.”

Answer options:

“2,000 and 3,000

“3,000 and 4,000

“4,000 and 5,000”

I’m not ready to solve yet. I need to think about how to estimate the average mass. What’s annoying about this problem?

  • A lot of data points
  • The graph changes: one part is very steep and the other tapers off almost into a straight line.

If they’d asked me for the average just from point C to age 30, I could estimate that easily, since it’s almost a straight line. But that steep part …

Hmm. Actually, I could think of the steep part, from A to C, as a second straight line. So I could estimate that part, too, and then average the two parts together.

The range A to C represents ages 12 to 20. In that 8-year timeframe (technically 9 data points), the mass goes from just under 1,000 to just over 5,000 in almost a straight line. So the average is right around 3,000 for that 8 years.

The range C to the end represents ages 21 to 30. In that 9-year timeframe (technically 10 data points), the mass goes from a little over 5,000 to about 5,600 … but most of the time it’s at the higher end of that range. So call that average around 5,500.

If we’ve got 9 data points at an average of about 3,000 and another 10 data points at an average of about 5,500, then the overall average is about halfway in between (but skewed a little bit higher than the exact middle point, since the T. rex spent an extra year at the 5,500 end of the scale).

Look at your answer options. Where is the mid-point of 3,000 and 5,500 going to fall? The average of 3,000 and 5,000 would be 4,000, so the actual average has to be north of 4,000 … and that’s good enough.

The correct answer for the first statement is 4,000 and 5,000.

Here’s the second statement again:

“The percent change in the mass from age 12 to age 16 is approximately _______________ the percent change in the mass from age 16 to age 20.”

And the answer options:

“equal to

“2 times

“3 times”

The statement is confusing enough that it’s a good idea to separate it into parts to try to understand each discrete piece.

First part: percent change in mass from 12 to 16

Second part: percent change in mass from 16 to 20

Third part: Is the first part (equal to, 2x, or 3x) the second part?

Okay, first find the percent change for the mass from ages 12 to 16—and remember: we can estimate heavily.

At A = 12 years, the average mass is about 1,000. At B = 16 years, it’s about 3,000.

Percent change is calculated by taking the difference and dividing by the original:

diff/orig=2000/1000

That’s the equivalent of 200 / 100 or 200%. The percent change for the first part is 200%.

Next, find the percent change for ages 16 to 20. At B = 16 years, the average mass is about 3,000. At C = 20 years, it’s about 5,000.

The difference is 2,000 again … oh, and here’s a trap! They’re hoping people will think they just asked about the difference period, not the percent change. In that case, it would be true that the difference for the first period is about equal to the difference for the second period—but that’s not what they asked! Don’t pick the first answer.

Find the percent change:

diff/orig=2000/3000

That’s only 2/3 or about 67%.

Finally, the percent change of 200% is approximately how much bigger than the percent change of 67%? Or, more simply, 200 is approximately how much bigger than 67?

There are only two options left: either twice as big or three times as big. 200 is a lot more than twice as big as 67, so it must be three times as big.

The correct answer for the second statement is 3 times.

Key Takeaways for estimating on the EA:

(1) When they ask for an approximate answer, you can probably estimate. Verify by checking the answers. If they are decently far apart, not only can you estimate…you should estimate! Why do more work than you have to?

(2) How heavily can you estimate? Check how far apart the numbers are. In this case, we had to start out doing some real calculations (though, even then, with rounded numbers). Towards the end, we were able to avoid a lot of math because the answer choices were so far apart.

(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.

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