IR Explained: Q25: Exercising For Hours

August 6, 2012

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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.

While this bar graph comes with an explanation, it is still somewhat difficult to understand. The leftmost bar, with a height of 5, does not refer to 0 hours or 1 hours, it refers to "at least zero, and less than one." So 5 adults reported exercising at least zero hours, but less than one hour.

By the same reasoning, the next bar to the right, with a height of 3, means that 3 adults reported exercising for at least one hour, but less than two hours. This vagueness makes precise calculations impossible, a characteristic that one of the two questions will capitalize on.

25A asks for the "least possible value" of the average amount of exercise for the 25 respondents. As we've seen, each respondent is claiming an amount of exercise within a certain range--not a specific amount.

For the "least possible" mean, take each respondent's least possible number of hours. The 5 zero-to-ones are 0, the 3 one-to-twos are 1, the 2 two-to-threes are 2, and so on.

The sum of all the respondents' hours is as follows: 5(0) + 3(1) + 2(2) + 4(3) + 4(4) + 5(5) + 1(8) + 1(10) = 0 + 3 + 4 + 12 + 16 + 25 + 8 + 10 = 78. Since there are 25 respondents, the average is 78/25, or 3 3/25. Don't worry about the precise decimal conversion--given the options available, it must be 3.12.

25B is not nearly so involved. Half an hour per day is 3.5 hours per week. Thus, anyone who exercised less than three hours definitely averaged less than one-half hour per day. That encompasses the leftmost three bars: 5 0-to-1s, 3 1-to-2s, and 2 2-to-3s, for a total of 10.

The 4 3-to-4-hour respondents might average less than one-half hour day, or they might average more. Thus, the total could be as little as 10, or as many as 14: between 10 and 14, inclusive.

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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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