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