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Free GMAT Graphics Interpretation Practice Question

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Patients treated in each of six waiting-time bins, in minutesSix bars over ordered waiting-time bins; bar height is the number of patients in that bin.0336699132165300 to 158015 to 3015030 to 458045 to 604060 to 752075 to 90Number of patients

The histogram below shows the number of patients a hospital emergency department treated last month in each of six waiting-time bins, in minutes. The bins are 0 to 15, 15 to 30, 30 to 45, 45 to 60, 60 to 75, and 75 to 90, where each bin includes its lower bound and excludes its upper bound. A total of 400 patients were treated. Select from each drop-down menu to complete the statement so that it is most accurate according to the data shown.

The bin containing the lower quartile of waiting times, the value below which one quarter of the patients fall, was the minute bin, and the number of patients in that bin was patients.

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Answer & Explanation

Correct answer

1: 15 to 30 · 2: 80

The lower quartile is the waiting time below which one quarter of the patients fall. One quarter of 400 patients is 100 patients, so you need the bin that the 100th patient lands in when you order every patient from shortest wait to longest. Add the bar heights from the left and watch where the running total reaches 100.

The first bin, 0 to 15 minutes, holds 30 patients, so after it the running total is 30, still short of 100. The second bin, 15 to 30 minutes, holds 80 patients, bringing the running total to 110, which passes 100. So the 100th patient lands inside the 15 to 30 bin, the lower quartile falls in the 15 to 30 minute bin, and that bin holds 80 patients.

The trap is to reach for the tallest bar. The 30 to 45 minute bin towers over the others at 150 patients, and it is easy to assume the quartile must live in the busiest bin. But height tells you how many patients share a bin, not where the one-quarter mark falls. By the time you enter the 30 to 45 bin the running total is already 110, past 100, so the quartile has come and gone. Accumulate to the quarter-count rather than picking the tallest bar, and the answer is the 15 to 30 bin with 80 patients.