6 day local trade show

[msbelasco]

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.

Answer c

Can someone please explain to me how to solve these types of questions. Thanks!

[ssidda01]

A is indeed right. I take back my earlier comment.

[neelgandham]

ms belasco - Are you sure that OA is C

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?

The question can be rephrased to: Is the total number of people registered during the event greater than 540 ?

(1) For the 4 days with the greatest number of people registered, the average (arithmetic mean) number registered per day was 100.

Total number of people who registered during these 4 days = 4*100 = 400.
Least number of people who registered during the remaining 2 days = 80*2 = 160.(Since, 80 is the least number of people registered in a single day).
Minimum number of people who registered during the show = 400 + 160 = 560.
So, the number of people who registered during the show > 560> 540.

Statement I is sufficient to answer the question.

(2) For the 3 days with the smallest number of people registered, the average (arithmetic mean) number registered per day was 85.

Total number of people who registered during these 3 days = 3*85 = 255 = 80 + 87 + 88.
Least number of people who registered during the remaining 3 days = 89(Since 88 falls in the least category (in red), the next highest value is 89)*3 = 267
Minimum number of people who registered during the show = 255+267 = 522.
The total number of people who registered during the show > 522.
So, the total number of people who registered can be either less than 540(say 525, 525 > 522)or be more than 540(say 590, 590 > 522).

Statement II isn't sufficient to answer the question.

IMO A

[GMATGuruNY]

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.

Answer c

Can someone please explain to me how to solve these types of questions. Thanks!

Statement 1: For the 4 days with the greatest number of people registered, the average (arithmetic mean) number registered per day was 100.
For 4 of the days, the average per day = 100.
For the other 2 days, the least possible average per day = 80.
Since there are MORE days with an average of 100 per day than with an average of 80 per day, the average for all 6 days must be CLOSER to 100 than to 80.
Thus, the average for all 6 days must be greater than 90.
SUFFICIENT.

Statement 2: For the 3 days with the smallest number of people registered, the average (arithmetic mean) number registered per day was 85.
If there are 3 days with an average of 85 per day and 3 days with an average of 86 per day, then the average for all 6 days will be less than 90.
If there are 3 days with an average of 85 per day and 3 days with an average of 1000 per day, then the average for all 6 days will be greater than 90.
INSUFFICIENT.

The correct answer is A.