Integrated Reasoning - Turn the Tables

Quarter Wit, Quarter WisdomStarting today, for the next few weeks we would like to focus on the ‘Integrated Reasoning’ section of the GMAT. The 1.5 yr old section of the GMAT has been giving jitters to many people. We have come across people with 48+ Quant scores but a 2/3 on the IR section. In my opinion, that’s a little strange. If you have strong reasoning skills, there is no reason you cannot apply those to this section as well.

If you are comfortable with the rest of the GMAT but get nightmares thinking of the IR section, I think the problem is psychological – that’s not to say that there is no problem – there is, but it can be easily remedied. In the next few posts we will see how the IR section is also based on the same fundamentals that we have been playing with all along.

There are different types of questions you get in the IR section. We will take Table Analysis today. The good thing about table analysis is that it requires close to 0.0 calculations to arrive at the answer. We know we keep talking about how GMAT Quant questions don’t require any calculations but IR table analysis honestly requires almost none. The question may seem to ask you to sum 10 big numbers but actually you don’t need to do that. Estimates will be more than sufficient in any case. We will discuss a complicated table analysis question today and if you are comfortable with this, you will be comfortable with most table questions.

Table Analysis Question:

Which of the following conclusions can be drawn from the table?

1. The state with the highest ‘number of candidates appeared’ in 2009 also had the lowest pass percentage in 2009.

Let’s sort the data by ‘2009-Appeared’. When put in increasing order, we get Wyoming at the bottom with number of candidates who appeared in 2009 as 496958.

The pass percentage of Wyoming is approximately 200/500 = 40%. Now we need to find whether there is any state with a lower pass percentage. Obviously we cannot and will not calculate the pass percentage of every state. Let’s analyze the 2009 data and group the pass percentage into 2 camps – greater than 50% and less than 50%. If we come across a pass percentage much much lower than 50%, we will give extra attention to it. Note that it is very easy to group them into >50% or <50%. E.g. In Iowa 203587 people appeared and 146084 passed. Since number of candidates who passed is more than 100000, the pass percentage is obviously more than 50%. Ignore it. Similarly, carry on till you reach Florida. 67036 is much less than 50% of 235451. In fact, it will be less than 30% since 10% of 235451 will be approximately 23000 and 30% will be 69000. Hence pass percentage of Florida is less than pass percentage of Wyoming. This means the given statement is false.

2. In 2010, all states experienced an increase in the ‘number of candidates appeared’ but the increase was not more than 16.2% for any state.

This might look ominous. Will we need to calculate the percentage increase for some states accurately up to one decimal place? We will follow the proverbial ‘cross the bridge when you come to it’. First let’s figure out whether all states experienced an increase in ‘the number of candidates appeared’ in 2010. Compare the 2010 values with 2009 values. We see an increase till we reach Michigan. The number of candidates appeared has decreased slightly in Michigan in 2010. This means the statement is false. No further analysis is required! We didn’t have to go to the bridge at all, much less cross it!

3. The state with the maximum number of passed candidates in 2011 is also the state with the minimum number of passed candidates in 2008.

First we sort the data by ‘2011-Passed’. We get Indiana at the bottom with 281565 passed candidates in 2011. Next, sort by ‘2008-Passed’. If Indiana is the state with the minimum number of passed candidates in 2008, it should appear at the top of the table now. It does! So the given statement is true.

4. The same state had the maximum pass percentage in every year.

Now this is tricky. We have to believe that the data must be such that we are able to get the answer in 2 mins. What kind of sorting could help us here? To get an idea of relative values of pass percentages, let’s sort the data by 2008-Appeared. The reason for that is that similar values will come together. States with 200k – 300k candidates will be together, those with 300k-400k candidates will be together etc.

Georgia appears at the top. We see that its pass percentage in 2008 was around 75% (15/20) which is quite high. Let’s look at the pass percentages of other states in 2008. Note that ‘the number of passed candidates’ doesn’t increase much by states but ‘the number of candidates appeared’ keeps increasing. Kansas, Michigan and Wyoming come closest with about 60%. No other state comes even close. So Georgia does have the highest pass percentage in 2008. Let’s focus on Georgia then. In all years thereafter it seems to have very high pass percentage except in 2012 when its pass percentage drops to about 50%. Now all we have to do is find a state with pass percentage more than 50% in 2012 to prove this statement to be wrong. We can easily see that Idaho (13/20) has a pass percentage much higher than 50%. Hence this statement is false.

Hope you learnt some tricks of the trade of tackling tables. More to come shortly!

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!

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