{"id":15810,"date":"2020-06-16T12:08:36","date_gmt":"2020-06-16T12:08:36","guid":{"rendered":"https:\/\/www.manhattanprep.com\/gmat\/?p=15810"},"modified":"2020-06-17T13:59:21","modified_gmt":"2020-06-17T13:59:21","slug":"executive-assessment-math","status":"publish","type":"post","link":"https:\/\/www.manhattanprep.com\/gmat\/blog\/executive-assessment-math\/","title":{"rendered":"Math on the Executive Assessment"},"content":{"rendered":"

\"Manhattan<\/p>\n

The Executive Assessment (EA) shares a lot of roots with the GMAT, GMAC\u2019s flagship graduate business school exam. In certain ways, the Executive Assessment feels almost like the GMAT on steroids\u2014it\u2019s even <\/span>more<\/span><\/i> stereotypically GMAT-like than the GMAT itself, if that\u2019s possible.<\/span><\/p>\n

One of those ways has to do with the way in which you can solve math problems. Most of the same math content areas are tested on the Executive Assessment, but a higher proportion of released Executive Assessment problems share a certain characteristic: You can use general \u201c<\/span>Fast Math<\/span><\/a>\u201d principles to make your job much easier\u2014and you can do even more with the overall Fast Math idea on the Executive Assessment.<\/span><\/p>\n

Here\u2019s the overall idea: Don\u2019t do math <\/span>that<\/span><\/i> you don’t have to. Don\u2019t do math <\/span>until<\/span><\/i> you have to. Before you actually do something you think you need to do, lay it out and ask yourself what the best path is through the math\u2014giving heavy consideration to estimation and other shortcuts.<\/span><\/p>\n

Let\u2019s try some problems out and see how this really works! All problems in this series are from the free problem sets that appear on the official Executive Assessment website<\/a>.<\/span><\/p>\n

EA Math Practice Question #1<\/b><\/h3>\n

Give yourself two minutes to complete this first problem. As of September 2017, it appeared as question 2 in the free online Quant Problem Solving problem set.<\/span><\/p>\n

The table below represents the combined net income of all United States companies in each of five sectors for the second quarter of 1996. Which sector had the greatest net income during the first quarter of 1996?<\/span><\/em><\/p>\n

\"Manhattan<\/p>\n

(A) Basic Materials<\/span><\/em><\/p>\n

(B) Energy<\/span><\/em><\/p>\n

(C) Industrial<\/span><\/em><\/p>\n

(D) Utilities<\/span><\/em><\/p>\n

(E) Conglomerates<\/span><\/em><\/p>\n

Got your answers? Even if you\u2019re not sure, guess\u2014that\u2019s what you want to do on the real Executive Assessment, too, so practice that now (even if your practice consists of saying, \u201cI have no idea, so I\u2019m randomly picking B!\u201d). <\/span><\/p>\n

Ready? Let\u2019s do this!<\/span><\/p>\n

The first order of business is to understand what the question wants and what the table tells you.<\/span><\/p>\n

\"Manhattan<\/p>\n

There are 5 sectors. Each one shows a certain net income for the second quarter and then a percent change from the first quarter. What\u2019s the significance of a negative vs. positive percent change?<\/span><\/p>\n

Think in terms of real business. If your division had a net income of 4.83 billion this quarter, but that represents a \u201326% change from last quarter\u2026then last quarter was better and this quarter your boss might not be very happy.<\/span><\/p>\n

Okay, now what do they want to know? Which sector had the greatest net income in the <\/span>first<\/span><\/i> quarter\u2026 hmm. So we\u2019re going to have to backwards-engineer this somehow.<\/span><\/p>\n

Start by jotting down the starting point for each sector and whether that one was higher or lower in the first quarter:<\/span><\/p>\n

BM: 4.83, \u201326%….Q1<\/span>\u2191<\/span><\/p>\n

E: 7.46, +40%…….Q1 <\/span>\u2193<\/span><\/p>\n

I: 5, \u20131%……………..Q1 <\/span>\u2191<\/span><\/p>\n

U: \u00a08.57, +303%..Q1 <\/span>\u2193<\/span><\/p>\n

C: 2.07, +10%…….Q1<\/span>\u2193<\/span><\/p>\n

They want to know which one was the highest once we back out the numbers. Sector C is already the lowest by far and it was even lower last quarter, so it\u2019s not that one. Eliminate answer (E).<\/span><\/p>\n

Sector I only went down by 1% in the second quarter, so basically it was still at about 5 in the first quarter. Call that your baseline point and test the other answers against it.<\/span><\/p>\n

Was Sector BM above or below 5 in the first quarter? The 4.83 figure reflects about a 25% decline from the previous quarter.<\/span><\/p>\n

\"Manhattan<\/p>\n

If 4.83 represents about a 25% decline from Q1, then it represents about 75% <\/span>of<\/span> Q1. Use this to estimate the value for Q1: If the 4.83 figure is about 75%, then what would 25% be?<\/span><\/p>\n

You would divide 75% by 3 to find 25%, so do the same with the value 4.83. <\/span><\/p>\n

4.83 is kind of annoying to divide. Try a number that seems like it\u2019s in the ballpark, like 1.5. (1.5)(3) = 4.5, so the value is around 1.5 (but really a little larger). The 1.5 estimate, then, is on the low side. Keep track of that.<\/span><\/p>\n

\"Manhattan<\/p>\n

Then, multiply by 4 to find 100%: (1.5)(4) = 6. The value is really a little larger than 6, since 1.5 is a low estimate.<\/span><\/p>\n

Therefore, sector BM, at 6+, was more than sector I, at 5; eliminate answer (C). Your new baseline point is 6+. Test the remaining answers against this number.<\/span><\/p>\n

The other two sectors were both lower in Q1. For sector E, 7.46 reflects a 40% increase from Q1. What if the starting number for this sector were 6? What would a 40% increase be?<\/span><\/p>\n

6 + 40% of 6<\/span><\/p>\n

To find 40%, find 10%, then multiply by 4. Then add your starting point of 6 back in:<\/span><\/p>\n

(6)(0.1) = 0.6<\/span><\/p>\n

(0.6)(4) = 2.4<\/span><\/p>\n

6 + 2.4 = 8.4<\/span><\/p>\n

If Q1 were 6, then this sector would have been at 8.4 in the second quarter. It wasn\u2019t; it was only at 7.46. Sector E, therefore, was not as high as sector BM, so eliminate choice (B).<\/span><\/p>\n

Finally, sector U started at 8.57, but that represented a whopping 303% increase over Q1! If you started at 6 and increase that number by 300%, it would be way over 8.57. Sector U also must have started lower than 6, so eliminate choice (D).<\/span><\/p>\n

The Basic Materials sector is the last one standing. The correct answer is (A).<\/span><\/p>\n

You could have done all of the above with very precise calculations\u2014but that\u2019s really annoying when you don\u2019t have access to a calculator or Excel. Note that you didn\u2019t actually have to make very precise calculations because the problem was set up to allow you to estimate even though it didn\u2019t tell you that you could.<\/span><\/p>\n

The beauty of the Executive Assessment is that this is a <\/span>business<\/span><\/i> test, not a <\/span>math<\/span><\/i> test. They\u2019re not interested in knowing whether you can do precise math calculations on paper. They\u2019re interested in knowing whether you have a general number sense that allows you to reason your way to a conclusion\u2014we call that the \u201cback of the envelope\u201d approach. All my boss really needs to know is which division did best last quarter, not what the exact numbers were, so I can just do a quick-and-dirty approach that addresses the big picture. <\/span><\/p>\n

Key Takeaways for Executive Assessment Fast Math<\/b><\/h4>\n

(1) You often don\u2019t need to calculate exact values. Look for opportunities to estimate and do back-of-the-envelope calculations wherever possible.<\/span><\/p>\n

(2) You\u2019re going to need to practice that! First, you need to get yourself into the mindset that the Executive Assessment isn\u2019t a math test and you actually aren\u2019t just trying to calculate, calculate, calculate. Second, you\u2019re going to need to spend time thinking about how to back-of-the-envelope something in various different situations.<\/span><\/p>\n

(3) Turn that knowledge into Know the Code flash cards:<\/span><\/p>\n

\"Manhattan<\/p>\n

EA Math Practice Question #2<\/b><\/h3>\n

Here\u2019s another Executive Assessment problem from the official free practice set (this one is labeled #3 in the PS set on the Executive Assessment website, as of September 2017):<\/span><\/p>\n

According to the table below, the number of fellows was approximately what percent of the total membership of Organization X?<\/span><\/em><\/p>\n

\"EA<\/p>\n

(A) 9%<\/span><\/em><\/p>\n

(B) 12%<\/span><\/em><\/p>\n

(C) 18%<\/span><\/em><\/p>\n

(D) 25%<\/span><\/em><\/p>\n

(E) 35%\u201d<\/span><\/em><\/p>\n

Before we dive in, what principles do you remember from our discussion of the first Executive Assessment problem?<\/span><\/p>\n

Think about it.<\/span><\/p>\n

Keep thinking about it.<\/span><\/p>\n

Don\u2019t read below yet.<\/span><\/p>\n

Okay, here are some things I remember. \u263a Don\u2019t do math unless \/ until I have to. If I do have to do some calculations, lay things out first, then look at everything to decide what the best path is (and to see whether I can spot any shortcuts!).<\/span><\/p>\n

These principles are reflected in the below graphic:<\/span><\/p>\n

\"EA<\/p>\n

When a new Executive Assessment problem first pops up, I glance: What have I got, big picture? Without reading the full text, I can see the following things: a table\u2026with some fairly annoying numbers. Also, the answers are percentages, so this is a percent problem of some kind.<\/span><\/p>\n

The annoying numbers are making me wonder whether I\u2019ll be able to estimate. I\u2019m going to keep an eye out for that possibility as I go to my next step, Read.<\/span><\/p>\n

Yep, it\u2019s a percent problem. What do they want? Jot it down.<\/span><\/p>\n

\"EA<\/p>\n

Don\u2019t start solving yet! Go to the second row: Reflect & Organize.<\/span><\/p>\n

\"EA<\/p>\n

Glance at the Fellows number. Annoying. And then the total? I have to add that up. Ugh.<\/span><\/p>\n

Look at the answers again. The bottom three are decently far apart\u2014estimation would probably be close enough.<\/span><\/p>\n

(A) 9%<\/span><\/p>\n

(B) 12%<\/span><\/p>\n

(C) 18% \u2192 20% = 1\/5<\/span><\/p>\n

(D) 25% \u2192 25% = 1\/4<\/span><\/p>\n

(E) 35%\u201d \u2192 33.3% = 1\/3<\/span><\/p>\n

But answers (A) and (B) are both around 10%…hmm.<\/span><\/p>\n

I know! If it does seem to be between those two, then I can estimate whether the number is greater than 10% or less than 10%\u2014that\u2019s not a hard estimate to make.<\/span><\/p>\n

Great, now that I actually have an angle to solve, I can go ahead and do the work.<\/span><\/p>\n

Oh, wait, one more annoying part to consider: adding up the five numbers to get the total. I only need to estimate, so I can estimate the individual numbers, first of all. I can also try to put them together into \u201cpairs\u201d that add up to \u201cnice\u201d numbers. Okay, let’s do this.<\/span><\/p>\n

The first one is 78, which is almost 100. Look for another number that would \u201cpair\u201d well with 100: how about Associate Members, at 27,909? Add them up to get about 28,000, a \u201cnice\u201d number.<\/span><\/p>\n

Any others?<\/span><\/p>\n

\"EA<\/p>\n

9,200 and 2,300 equal 11,500, another nice-ish number.<\/span><\/p>\n

That leaves 35,500\u2014oh, let\u2019s pair that with 11,500 to get an even 47k. Then add in the 28k to get about 75k. Nice!<\/span><\/p>\n

Now, the top of the fraction is the 9,200 number. Maybe 9k is close enough. What\u2019s 9k \/ 75k? Or 9 \/ 75?<\/span><\/p>\n

Reflect for a moment again. Dividing that fraction is kind of annoying.<\/span><\/p>\n

I\u2019m trying to find a percent. Percent literally means \u201cof 100\u201d\u2014wouldn\u2019t it have been nice if the fraction had already had 100 on the bottom? SO annoying that it doesn\u2019t\u2026<\/span><\/p>\n

Hmm\u2026<\/span><\/p>\n

Is there any way to get that number on the bottom to be 100 instead of 75\u2026?<\/span><\/p>\n

What did we do with that 75% in the first problem (in the first installment of this series)? Go back and take a look.<\/span><\/p>\n

(Seriously, go look! See what, if anything, you can figure out on your own before you keep reading.)<\/span><\/p>\n

To go from 75% to 100%, take the 75% figure, divide by 3 to get 25%, then multiply by 4 to get 100%.<\/span><\/p>\n

BUT, if I\u2019m going to do that with the bottom of the fraction, then I have to do the same thing to the top of the fraction. I can manipulate a fraction in any way that I like as long as I do the same thing to the top and the bottom.<\/span><\/p>\n

So, take 9, divide by 3 to get 3, then multiply by 4 to get 12. Boom! The new fraction is 12 \/ 100. Look at the answers\u2014we have an exact match at 12%. \u263a<\/span><\/p>\n

The correct answer is (B).<\/span><\/p>\n

What did you learn on this Executive Assessment problem? Think about your takeaways before you read mine.<\/span><\/p>\n

Key Takeaways for Executive Assessment Fast Math<\/strong><\/h4>\n

(1) You often don\u2019t need to calculate exact values. Look for opportunities to estimate and do back-of-the-envelope calculations wherever possible.<\/span><\/p>\n

(2) Different problems might have some shortcuts in common; when you learn something on one problem, look for opportunities to apply that learning on different-but-similar-in-some-way problems. The 75% \u2192 100% thing doesn\u2019t require a table or even necessarily a story. It doesn\u2019t even need to be 75% to start\u2014it just requires you to know that you\u2019re trying to get to 100% from a number that\u2019s a little annoying.<\/span><\/p>\n

(3) Turn that knowledge into Know the Code flash cards:<\/span><\/p>\n

\"EA<\/p>\n

EA Math Practice Question #3<\/b><\/h3>\n

Our final practice question is labeled #4 in the PS set on the Executive Assessment website as of September 2017.<\/span><\/p>\n

\u201cThe regular price per can of a certain brand of soda is $0.40. If the regular price per can is discounted 15 percent when the soda is purchased in 24-can cases, what is the price of 72 cans of this brand of soda purchased in 24-can cases?<\/span><\/p>\n

\u201c(A) $16.32<\/span><\/p>\n

\u201c(B) $18.00<\/span><\/p>\n

\u201c(C) $21.60<\/span><\/p>\n

\u201c(D) $24.48<\/span><\/p>\n

\u201c(E) $28.80\u201d<\/span><\/p>\n

What did you think about this problem?<\/span><\/p>\n

\"EA<\/p>\n

I found it pretty annoying. \u263a I mean, sure, I didn\u2019t find it crazy hard to find the 15% discount off of $0.40:<\/span><\/p>\n

10% of 0.40 is 0.04\u2026<\/span><\/p>\n

another 5% is half of that, or 0.02\u2026<\/span><\/p>\n

so the discount is $0.06\u2026<\/span><\/p>\n

and the discounted price is $0.34<\/span><\/p>\n

And then I want to buy 72 cans, so it\u2019s just (72)(0.34)\u2026<\/span>aaagh,<\/span><\/i> but I don\u2019t have a calculator<\/span><\/i>.<\/span><\/p>\n

I refuse to do that out the long way. Seriously! There\u2019s got to be an easier way.<\/span><\/p>\n

Picture this: You\u2019re standing in the convenience store. You want to buy this soda. You\u2019ve just figured out that it\u2019s going to cost you $0.34 a can\u2026and you know you want 72 cans\u2026but you don\u2019t have a calculator on you (your phone died) and you don’t even have pen and paper. Also, you forgot your credit card. (It\u2019s been a long day.)<\/span><\/p>\n

So how are you going to figure out whether you have enough cash on you to buy all 72 cans?<\/span><\/p>\n

That\u2019s not a rhetorical question. Close your eyes, picture yourself there, and try to figure out what you\u2019d do.<\/span><\/p>\n

Thinking?<\/span><\/p>\n

Thinking?<\/span><\/p>\n

Okay, here\u2019s my idea. In the real world, I wouldn\u2019t literally need to calculate to the penny\u2014I\u2019d just need to estimate to make sure I have <\/span>enough<\/span><\/i> cash. But this is a math test and the answers are down to the penny\u2026so don\u2019t I have to calculate exactly here?<\/span><\/p>\n

Glance at the answers.<\/span><\/p>\n

If the answers had been of the variety $10.01, $10.02, $10.03\u2026, then yes, I\u2019d have to calculate to the penny. But they\u2019re not. They\u2019re each at least a couple of dollars apart, so I can estimate. How?<\/span><\/p>\n

Let\u2019s see. It\u2019s going to cost me $0.34 to buy one can. How many could I buy for a dollar?<\/span><\/p>\n

I can get 3 cans (basically\u2014technically, it\u2019ll cost me $1.02 for 3 cans, but close enough!). So 3 cans for $1\u2026how many do I want again? Oh yeah, 72 cans. So that\u2019s going to cost me about 72 \/ 3 = $24.<\/span><\/p>\n

Oh. Look at the answers. There\u2019s only one that\u2019s close\u2014answer (D). Done!<\/span><\/p>\n

You can also, by the way, do this same estimation from the math I set up before I got frustrated by my lack of a calculator: (72)(0.34). Just look at it in a different way, now that you\u2019ve realized you can estimate. Since 0.34 is about 1\/3, you’re just taking about one-third of 72…it\u2019s the same math! $24.<\/span><\/p>\n

What we just did is classic back-of-the-envelope math. You don\u2019t need an exact number\u2014you just need a quick-and-dirty, good-enough estimate. We certainly weren\u2019t allowed to do that on math tests in school, but the Executive Assessment is <\/span>not<\/span><\/i> a math test.<\/span><\/p>\n

Well, yes, it is, somewhat. But not in the way that you\u2019re used to from school. We do have to know various math formulas and rules, but the Executive Assessment is really mostly interested in how well you can reason about math. After all, in the real world, you\u2019re never going to be forced to do math on paper without the benefit of Excel or a calculator. But you are going to need to be able to think about mathematical concepts and draw conclusions\u2014not in the \u201cwhat\u2019s the answer to this math problem\u201d sense, but in a \u201cwhat should we do about this problem that our division is facing?\u201d sense.<\/span><\/p>\n

So, while the Executive Assessment looks a whole lot like a traditional math test, it really isn\u2019t at all. Most of the time, you can get to the answer through a combination of strategic approaches, like the back-of-the-envelope approach discussed above. That\u2019s what you\u2019re looking to learn and practice as you study for this exam.<\/span><\/p>\n

Key Takeaways for Executive Assessment Fast Math<\/strong><\/h4>\n

(1) You often don\u2019t need to calculate exact values. Look for opportunities to estimate and do back-of-the-envelope calculations wherever possible.<\/span><\/p>\n

(2) If the numbers in the problem or answers (or both!) seem annoying, there\u2019s probably an opportunity to estimate somewhere. Also, get in the habit of glancing at the answers to see how far apart they are (when they\u2019re just plain numbers)\u2014the farther apart they are, the better the opportunity to estimate.<\/span><\/p>\n

(3) Turn that knowledge into Know the Code flash cards:<\/span><\/p>\n

\"EA<\/p>\n

*Executive Assessment questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.<\/span><\/h6>\n

Can\u2019t get enough of Stacey\u2019s GMAT mastery? Attend the first session of one of\u00a0her upcoming GMAT courses<\/a>\u00a0absolutely free, no strings attached. Seriously.<\/strong><\/em><\/p>\n

\n

\"stacey-koprince\"<\/a>Stacey Koprince<\/a>\u00a0is a Manhattan Prep instructor based in Montreal, Canada and Los Angeles, California.<\/strong>\u00a0Stacey has been teaching the GMAT, GRE, and LSAT for more than 15 years and is one of the most well-known instructors in the industry. Stacey loves to teach and is absolutely fascinated by standardized tests.\u00a0Check out Stacey\u2019s upcoming GMAT courses here<\/a>.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

The Executive Assessment (EA) shares a lot of roots with the GMAT, GMAC\u2019s flagship graduate business school exam. In certain ways, the Executive Assessment feels almost like the GMAT on steroids\u2014it\u2019s even more stereotypically GMAT-like than the GMAT itself, if that\u2019s possible.<\/p>\n","protected":false},"author":6,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[928,52900,53128,873,2,4,8],"tags":[58180,52823,53022,58181,58182],"yst_prominent_words":[53997],"class_list":["post-15810","post","type-post","status-publish","format-standard","hentry","category-business-mindset","category-business-school","category-executive-assessment","category-for-current-studiers","category-how-to-study","category-mba-b-school","category-quant-on-gmat","tag-ea-math","tag-executive-assessment","tag-fast-math","tag-math-on-the-ea","tag-math-on-the-executive-assessment"],"_links":{"self":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/15810","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/comments?post=15810"}],"version-history":[{"count":5,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/15810\/revisions"}],"predecessor-version":[{"id":18968,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/15810\/revisions\/18968"}],"wp:attachment":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/media?parent=15810"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/categories?post=15810"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/tags?post=15810"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/yst_prominent_words?post=15810"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}