Manhattan 5lbs. Averages Q.39)

[kg2576]

A set of 7 integers has a range of 2, an average of 3, and a mode of 3.

A
The 3rd # in the set when the numbers are arranged in ascending.
B
The 5th # in the set when the numbers are arranged in ascending.

This question would appear to take a tremendous amount of time to figure out even one of the possibilities, no? The explanation states that one possibility is 2, 2, 2, 3, 4, 4, 4. What would be an efficient approach to figure this out?

Thanks, kg

[tommywallach]

Hey KG,

Eh. Not too long, because the fact that it's a range of 2 and an average of 3 means that it has to be made up entirely of 2s, 3s, and 4s, with at least 3 of one number. The sum also has to be 21.

2233344 -- there's one option
2223444 -- there's another

That took me about 2 minutes to work out, and now I've proven D.

I'm not trying to say it's easy, but I wouldn't say it's insane. : )

-t