IR Explained: Q26: Charting Ages

August 8, 2012

This post is part of a series--IR Explained--that walks through the sample Integrated Reasoning questions provided in the latest edition of the GMAT Official Guide.

This Graphics Interpretation question is as close as you'll get to pure math on the Integrated Reasoning section.

The pie chart breaks down a town's population into age groups: 20% are children 0-12 years of age, 25% are teenagers 13-19 years of age, and so on. Note that every age group is represented, making five groups in all.

26A asks you to compare "children or teenagers" to "seniors." Children represent 20% of the population while teenagers represent 25%, for a total of 45%. Seniors make up 17%.

Put another way, the question asks "45% is how many times 17%?" To answer, simply divide 45/17. In fractional terms, that's 2 11/17, or a bit more than 2.5. Only one possible answer is anywhere close: 2.65.

26B requires that you convert percentages into numbers. We're told that 540 is the difference between the number of people aged 39 and under and those aged 40 and over.

First, we need to find the difference in percentages. The percentage of townspeople aged 39 and under is 20% + 25% + 23% = 68%. That leaves 100% - 68% = 32% as the number aged 40 and over.

Thus, 68% - 32% = 36% is the difference between the two age groups. The question tells us that 540 is the difference, so 36% of the population is equal to 540. Put in algebraic terms:
540 = 0.36t
t = 540/0.36
t = 54000/36 [multiply top and bottom by 100]
t = (54/36)*1000 [factor out 1000 to simplify the comparison between 54 and 36]
t = (1.5)*1000 [divide 54 and 36 by 18]
t = 1500

If you were pressed for time, you could approximate and still likely end up with the right answer. Simply change 540 to 500 and 0.36 to 1/3:
500 = 1/3t
500(3) = t
1500 = t

Even if you didn't pick exactly the right numbers to approximate with, it would be unlikely to end up so far off to pick the other choices, such as 1,080 and 2,400.

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About the author: Jeff Sackmann has written many GMAT preparation books, including the popular Total GMAT Math, Total GMAT Verbal, and GMAT 111. He has also created explanations for problems in The Official Guide, as well as 1,800 practice GMAT math questions.

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