Predicting the USA’s World Cup Chances Tomorrow Using Integrated Reasoning

By this time tomorrow, the results will be in: will the United States have survived the Group of Death with Germany, Portugal, and Ghana? Or will Portugal’s late equalizer from Sunday have yanked the dream of Elimination play from the Yankees? A lot is riding on the concurrent USA vs. Germany and Portugal vs. Ghana matches tomorrow as all four teams have the potential to advance to the knockout stage of this year’s World Cup.

So much is at stake, actually, that some of the greatest minds in the world have dedicated time to breaking down all the possibilities; Nate Silver’s website gives the US a slightly better than 75% chance of moving through, with those possibilities including:

-An outright win against Germany
-A draw with Germany (around which a popular conspiracy theory is growing, given that a draw puts both teams through)
-A close loss to Germany with a Portugal win (but not blowout) over Ghana
-A close loss to Germany with more overall goals scored in the tournament than a victorious Ghana

Given all the situations – all requiring math, encompassing all the permutations available and including probabilities…all GMAT-relevant terms – some of these great minds have put together helpful infographics that can shed light on the scenarios…and help you study for the GMAT’s Integrated Reasoning / Graphics Interpretation section. How? Consider this infographic (click to enlarge):

This graphic has a lot of similarities to some you may see on the Integrated Reasoning section of the GMAT. It’s a “unique graphic” – not a standard pie chart, bar graph, line graph, etc. – so it includes that “use reasoning and logic to figure out what’s happening” style of thinking that you’ll almost certainly find on at least one Graphics Interpretation problem. And like many GI problems on the GMAT – even those classic bar graphs, etc. – this one has a potentially-misleading scale or display if you’re not reading carefully and thinking critically. Most notably:

If Nate Silver is right (as he usually is) and the US is better than a 3-1 favorite to advance, why is there so much red on this graph?!

And here’s where critical thinking comes into play:

1) What’s more likely – that both Germany and Ghana win 4-0, or that they each win 1-0? Soccer history tells us that 4-0 wins are quite rare, but 1-0 wins are fairly common. The blue Germany 1-0 / Ghana 1-0 box, though, is the same size as the red 4-0/4-0 box, making the scale here a little misleading. This graph does not incorporate probability into its cell size, so it treats all outcomes as equally likely, therefore skewing the red-vs-blue dynamic. On Integrated Reasoning, you may well have to consider a chart’s scale and determine whether it can accurately be extrapolated into something like probability!

2) This graph only expands “__________ side wins” into scores for three teams: Germany, Ghana, and Portugal. Why doesn’t it do so for the USA, or include the goals scored in a US-Germany tie? Likely because this graph is designed for an American audience, and the American side’s “what if?” scenarios are the same for *all* wins – if the US wins, it finishes #1 in the group and moves on – and for draws, in which the US would finish second. It’s only if the US loses that any other situations matter – by how much did the US lose? what was the score of the other match? – so in order to save space and draw attention to the meaningful “what ifs” this graph treats all US > Germany scenarios with one column. Which works for the purpose of this graph, but leads to another really misleading takeaway if all you’re looking at is blue vs. red – the blue columns for the US are wildly consolidated (and it’s all noted correctly so it’s not “wrong”), so you have to read carefully and think critically in order to understand what the graph truly displays.

Note that this is in no way a “misleading graphic” – it’s a well-constructed infographic to talk about all the possibilities that could happen and change US fortunes tomorrow. It’s just that the maker of the graphic chose to display the valid information in a certain way, one that may mislead the eye if the user is not being careful and thinking critically. That’s also very true of GMAT Integrated Reasoning – the graphics you see will be valid and meaningful, but you’ll need to read them carefully and think logically to avoid making assumptions or drawing flawed conclusions. And as this graphic shows, sometimes your mind’s initial reaction needs to be checked by some critical thinking.

So when you see Graphics Interpretation problems on the GMAT Integrated Reasoning section, be careful. What may seem obvious or too-good-to-be-true (like, it hurts to say, a 2-1 lead into the 95th minute) may require that little extra attention to detail to gain the result that you’re looking for, the one that gets you through to the next stage where you want to be.

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By Brian Galvin

2 Essential Strategies for GMAT Integrated Reasoning Questions

GMAT students can now benefit from a blog series featuring video tips from Veritas Prep’s own Director of Academic Programs, Brian Galvin. Previously, Brian helped students with Data Sufficiency, Sentence Correction, and Critical Reasoning.

Today, we’ll take a look at strategies that can help you excel on the Integrated Reasoning section of the GMAT.

These two simple strategies will help you when it comes time to answer two-part analysis questions on test day. Make sure to keep your work clean along the way, and hopefully that will add to your success with these questions.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter! For more videos, subscribe to our YouTube channel!

Integrated Reasoning – Two Part Analysis Questions

Quarter Wit, Quarter WisdomLet’s continue our series and look at another Integrated Reasoning question type today – two part analysis. As complicated as it sounds, it’s actually the simplest of the IR question types in my opinion. The reason for this is that it tests no new skills; it checks your ability to handle the same old PS and CR questions.

The only reason it is new is that it reduces the probability of guessing correctly and it puts more time pressure on you! Your probability of guessing correctly is 20% in PS/CR questions; it goes down to 4% in two part analysis because you have to guess correctly twice. As for time pressure, you get about 2 mins for every PS and about 1.5 mins for every CR question. For each part of two part analysis, you have only 1.25 mins.

Anyway, let’s look at a sample question to get familiar with this question type.

Question: A grocery store sells fruits in pre packed closed bags such that individual pieces of fruit are not sold. Mangoes are sold at the rate of $5 per bag (each bag contains two mangoes) and apples at the rate of $8 per bag (each bag contains five apples). During a particular day, the store started with some mangoes and apples and sold them all by the end of the day. The revenue at the end of the day from selling mangoes and apples that day was $128. Which of the following could represent the number of mangoes and the number of apples that were in the store at the beginning of that day?

Choose only one from each column:

 

 

Solution:

Note that it is a PS question. Only the format of the question is different. Also, the use of the word ‘could’ in the question stem suggests that there could be multiple solutions to this problem. Let’s take a closer look at how to solve it.

Say, number of bags of mangoes is ‘m’ and number of bags of apples is ‘p’.

Then 5m + 8p = $128 (total revenue)

Each bag of mangoes has 2 mangoes and each bag of apples has 5 apples.

So number of mangoes sold = 2m (to be selected in the first column)

Number of apples sold = 5p (to be selected in the second column)

We need to solve for this equation: 5m + 8p = 128

It is easy to see that one solution to this equation is m = 0, p = 16. The next solution will be m = 8, p = 11. Another will be m = 16, p = 6. Yet another will be m = 24, p = 1. If you are wondering how we are landing on one solution after another so effortlessly, you need to check out a previous post of QWQW – Integral Solutions to Equations in Two Variables.

So there are three solutions possible to our question: Which of the following could represent the number of mangoes and the number of apples that were in the store at the beginning of that day?

There are three different cases possible:

Case 1: Number of mangoes sold could be 16 (= 2m when m is 8). In that case number of apples sold will be 55 ( = 5p when m is 8, p is 11)

Case 2: Number of mangoes sold could be 32 (= 2m when m is 16). In that case number of apples sold will be 30 ( = 5p when m is 16, p is 6)

Case 3: Number of mangoes sold could be 48 ( = 2m when m is 24). In that case number of apples sold will be 5 (= 5p when m is 24, p is 1)

The case we select should be that of which both numbers are included in the options. Case 3 satisfies this condition. So we select 48 in the first column and 5 in the second column.

This is the only ‘exotic’ step of the two part analysis. The rest of the question is just like any other PS question.

Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!

GMAT Testing Volume: A Deeper Look into the Numbers

Last week Poets & Quants ran an article announcing robust growth in GMAT testing volume from Testing Year 2011 to 2012. A total of 286,529 exams were taken in Testing Year 2012, representing the highest total ever, and 11% growth vs. the previous year. (GMAC’s testing years run from July 1 to June 30 each year.) While testing volume in the United States is still down about 10% vs. Testing Year 2009, strong growth in East and Southeast Asia helped drive total testing volume to its highest level ever.

Sounds like the GMAT and the graduate management education market are firing on all cylinders, right? While we agree that reports of the death of business schools have been greatly exaggerated, there is a huge part of the story here that everyone is missing, one that will almost certainly bubble up once we see Testing Year 2013 numbers from GMAC later this year.
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Test Prep and Admissions: The Best of 2012

Believe it or not, 2012 is almost over. If you’re reading this, it means that the world hasn’t ended, and that at least some of us still have electricity and Internet access, so we’re ending on a good note! As we at Veritas Prep wind down the year, we thought we’d share some of our biggest news, best posts, and most interesting topics from the past 12 months.

We hope that this blog has provided you with some useful insights as you’ve studied for the GMAT or SAT, or as you have slaved over your applications. Sometimes we have a little fun, and sometimes we veer off topic to talk about what interests us, but everything written here comes from the same place: We want to help you be successful in your pursuit of admissions success!
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One More Reason Not to Sweat Integrated Reasoning

Last week the Stanford GSB admissions team wrote a blog post that gives business school applicants one more reason to calm down about the new Integrated Reasoning section on the GMAT. Simply put, the Stanford admissions team will not take applicant’s Integrated Reasoning scores into account when making their decisions for the 2012-2013 application cycle.

“Wait, why wouldn’t they use it if the people behind the GMAT went through all the trouble to create it?” you may be asking. Don’t take this as a sign that Stanford or any other MBA program does not believe in the new Integrated Reasoning section. Instead, think about how much history MBA admissions officers have with the “old” GMAT… The Stanford admissions team alone looks at thousands and thousand of them every year. Now, a new number shows up on the report, and they need to get comfortable with that number before they can make life-changing decisions based on it.
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First Integrated Reasoning Score Percentiles Released!

This week the Graduate Management Admission Council (GMAC) released its first percentile table for Integrated Reasoning scores, based on GMATs taken since June 5, when the new Integrated Reasoning section launched. As GMAC explains on the mba.com website, these percentiles will be updated monthly for the remainder of 2012. After that, Integrated Reasoning percentiles will be updated on the same schedule as percentiles for the other sections of the GMAT.

Why the frequent updating? Integrated Reasoning is still so new that every new wave of test takers can have a noticeable impact the overall pool. For the other, more established sections of the GMAT (which are taken about 300,000 times per year), percentiles will move very slowly and subtly. But, when only ten thousand or so students have taken the test, these percentile numbers may keep moving around a bit (especially as test takers become more familiar with the new section), and GMAC wants to recognize that fact by adjusting its numbers frequently.
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Integrated Reasoning Isn’t Coming… It’s Here!

This is the day everyone has been anticipating for nearly two years now: Today the Graduate Management Admission Council (GMAC) launched the new Integrated Reasoning section of the GMAT. While we’ve made our point of view on Integrated Reasoning perfectly clear in this space multiple times, it is definitely worth noting that you are absolutely not at risk assuming that you take the test today or later.

Why? Because a drastic change in the test from last week to this week would make all sorts of comparisons difficult and threaten the validity of the exam, and that’s the last thing that GMAC and its member business schools want. GMAC has already made plenty of Integrated Reasoning prep resources available. The last thing they want is for a wave of people to walk into testing centers without having any idea about what Integrated Reasoning is!
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Integrated Reasoning? The Whole GMAT Is About Reasoning!

All of the hoopla leading up to the introduction of the GMAT’s new Integrated Reasoning section makes this month feel very much a part of 2012. Every four years we hear all about the summer Olympics, and then roll from that right into the U.S. presidential elections… And don’t forget that it’s a leap year.

It seems that the world saves special events for years that are divisible by four, and GMAC went along with the plan by waiting until 2012 to introduce its biggest change to the GMAT is nearly two decades. The new Integrated Reasoning section goes live on June 5, but judging by all of the chatter, it feels like it’s been here for months already. “Why the big change to the test?” everyone has been asking.
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