mehravikas wrote:S18-16 During a 6-day local trade show, the least number of people registered in a single day was 80. Was the average (arithmetic mean) number of people registered per day for the 6 days greater than 90?
(1) For the 4 days with the greatest number of people registered, the average (arithmetic mean) number registered per day was 100.
(2) For the 3 days with the smallest number of people registered, the average (arithmetic mean) number registered per day was 85.
We need to know whether the average over six days was greater than 90. This is equivalent to: did more than 540 people attend the show?
From 1), we know that on four days we had 400 people, and on the other two days, from the stem, we had at least 160 people, so we surely had at least 560 people. Sufficient. (jsl- I think you assumed it was a 5-day show in your calculations above)
From 2), we only know that, on the three days with the lowest attendance, the average was 85- that is, on those three days, we had 255 people in total. On one day there were 80 people; we must have had 175 people on the other two. We might have had:
{80, 87, 88, 89, 89, 89}
and not only might the average be less than 90; there might not have been a single day where 90 people registered for the show. Or, of course, we could have an average as high as we like:
{80, 85, 90, 1000000, 1000000, 1000000}
So 2) is not sufficient.
________
If the number in Statement 2) were larger, the statement might become sufficient. If you change '85' to '88', you can be sure that the average per day is at least 90 (but not necessarily greater), and if you change it to '89', you can be certain the average per day is greater than 90. It's not a statement that should be dismissed too quickly, since it does give you information about all elements in the set.
