The range of the monthly numbers of customers at a certain store was

Question

The range of the monthly numbers of customers at a certain store was 240 for the year 1999 and 320 for the year 2000. Which of the following is the smallest possible range of the monthly numbers of customers at the store for the two-year period 1999-2000 ?

A. 80
B. 240
C. 320
D. 400
E. 560

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Bunuel · Accepted Answer

Since the range is the difference between the highest and lowest numbers, the smallest possible two-year range can't be less than the largest yearly range. The largest range of a single year is 320 (for 2000), so the smallest possible range for the two years is also 320. Answer: C. Similar question from GMAT Prep Focus: https://gmatclub.com/forum/each-employe ... 25045.html Hope it helps.

DanTheGMATMan · Answer

The overall range can't be any less than any of the individual ranges. In this case, constrained by the range of 320. Another similar question: https://gmatclub.com/forum/three-people ... l#p1212587

shashank07! · Answer

Do we have any similar approach for calculating maximum range as well?

Bunuel · Answer

Theoretically, there’s no upper limit to the maximum range. For instance, in 1999, the lowest number of customers could have been 0, while the highest could have been 240. Then, in 2000, the maximum number could have been as high as 1,000,000 (with the lowest being 1,000,000 - 320). In this case, the range would be 1,000,000 - 0 = 1,000,000. So, by increasing the highest number for the year 2000, we can increase the range as much as we want.

Hope it's clear.

eaat · Answer

Can someone explain why 80 is wrong? I wrote in my notes for the year 1999 that the range could be from 10 to 250, so the range is 240. In the year 2000, it could range from 10 to 330, so the range is 320. The range between the two would be 330 minus 250, which is 80, right? I guess now that I'm reading it, the range here would be between 10 and 330; it should be 320. In this case, should we just assume the range is always the least range is always the bigger one of

Bunuel · Answer

The confusion is that you treated the two yearly ranges as if they were two separate intervals and then compared only their upper ends. But the question asks for the range of the entire two-year set, meaning all 24 months are placed into one group. Once you combine the groups, the range must run from the single lowest month anywhere in those two years to the single highest month anywhere in those two years, so the combined range can never be smaller than the bigger yearly range.

The range of the monthly numbers of customers at a certain store was

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The range of the monthly numbers of customers at a certain store was

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