Like high school seniors across the country, we at Veritas Prep are already well within our countdown-to-June period as we anxiously await the unveiling of the GMAT’s new Integrated Reasoning (IR) section (less than four months to go! Seniors/GMAT enthusiasts whoooo!) If you’re similarly-minded and thinking about the IR section already, the following should help you set your mathematical mind to the right frequency. Remember this: while the numbers in many IR problems might be large and specific, the math is all relative.

On the IR section, you will face 12 “problems”, each with more than one “question”, in 30 minutes. Using Relative Math (the theme for this post), you can determine that you’re looking at around a minute or so per question… which isn’t all that much time to interpret the question, perform lengthy calculations, and (discount) double-check your answer. Even with the use of the relatively-primitive IR calculator — one that does not recognize order-of-operations, so you will need to keep track of values by hand — these calculations will take time and leave potential for error. In most situations, you will want to avoid technical calculations unless they are absolutely necessary. Instead, you will want to employ Relative Math:

- Determine which values are relevant to a correct answer
- Estimate those values whenever possible
- Calculate values only when the estimates are too close to call
- Remember that the logical setup for the values is typically the crux of the question, not the calculation itself

As an example, consider the question:

City Amount Saved Total Budget Andersonville $8,225 $47,975 Bronxtown $16,750 $142,950 Chadwick $3,925 $20,325 Dodgeville $3,350 $16,275 Edgewater $13,100 $51,675 The table above shows the 2010 annual budget for the Sanitation Departments of five cities, and the amount of money that each was able to save over that budget for the 2011 fiscal year. Which city had the lowest percentage savings on the basis of the previous year’s budget?

- Anderson
- Bronxtown
- Chadwick
- Dodgeville
- Edgewater

Note that a calculator might be tempting in this case, but that each calculation requires you to key at least nine digits — a time-consuming process that raises your potential for typo-based error. An eye for both logical setup and Relative Math can guide you through this process efficiently and confidently. First, note the correct relationship — the lowest percentage savings, or the lowest savings-to-budget ratio. Your goal, then, is to test the ratios of left column to right, looking for the smallest ratio. Your “baseline” for Andersonville is approximately 8/48 or 1/6. And in relation to 1/6, you know that the numerator is a little over 8 and the denominator is a little less than 48, so the overall ratio is going to be slightly greater than 1/6. You can denote this quickly on your noteboard with a + sign or a > sign to help you recognize the direction of your estimates.

- >8/48, so >1/6
- <20/140, so <1/7 (the current “leader” in smallest ratio)
- <4/20, so <1/5
- >3/16, and since you’re comparing against 1/7 (or 3/21) you know that this is greater
- >13/52, so >1/4

The answer must be B, and if you’ve employed the above estimates you won’t have had to perform any true calculations to get there. Bronxtown had the lowest percentage savings.

Are you getting ready to take the GMAT? Take a look at some of the Integrated Reasoning sample problems our our site. And, as always, be sure to find us on Facebook and Google+, and follow us on Twitter!