rainbownlife wrote:please explain:
On her way home from work janet drives thru several toolbooths.Is there a pair of these toolbooths that are < 10 miles?
(1) first and last booths are 25 miles apart.
(2) janet drives thru 4 tool booths.
(1) by itself is insufficient, since there could be only 2 booths or there could be lots of booths. Maybe yes, maybe no.
(2) by itself is insufficient because we have no clue what the spacing is like.
However, if we know that there are 4 booths and the distance from booth 1 to booth 4 is 25 miles, we know that at least 2 of the booths have to be within 10 miles of each other. We do NOT need to assume even spacing.
With 4 booths, we have 3 "gaps" (i.e. from 1 to 2, 2 to 3 and 3 to 4).
25/3 = an average of 8 1/3 miles per gap. To get an average of 8 1/3, at least one of the gaps has to be 8 1/3 miles or less (if all 3 gaps were greater than 8 1/3, then the average would be greater than 8 1/3).
So, for example, the gaps could be 3 * 8 1/3; or the gaps could be 12, 12 and 1; or the gaps could be 1, 1 and 23; or an infinite number of other possibilies, but in EVERY case at least one of the gaps is less than or equal to 8 1/3 miles. Together the statements give us a definite yes: choose (c).
