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GMAT - Data Sufficiency - Statistics

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 ?

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 ?

Statement 1:

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

Statement 2:

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

 

Statement 1:

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

the average number of people registered for 4 days is 100

i.e. total number of people registered on those 4 days = 4*100 = 400

Minimum number of people registered = 80

for minimum possible average assume that the other two days has 80 registrations

mean = (400 + 80*2)/6 = 560/6 = 93.33 > 90

so the mean will be greater than 90. hence the statement is sufficient. 

 

Statement 1:

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

the average number of people registered for 4 days is 100

i.e. total number of people registered on those 4 days = 4*100 = 400

Minimum number of people registered = 80

for minimum possible average assume that the other two days has 80 registrations

mean = (400 + 80*2)/6 = 560/6 = 93.33 > 90

so the mean will be greater than 90. hence the statement is sufficient.