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GMAT - Data Sufficiency - Statistics

If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75 ?

If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75 ?

(1) None of the six numbers is less than 75.
(2) None of the six numbers is greater than 75.

Assume the numbers are A, B, C, D, E and F

Statement 1:

None of the six numbers is less than 75.

A>=75, B>=75, C>=75, D>=75, E>=75, F>=75 .... (i)

A + B + C + D + E + F >= 75*6

Average of 6 numbers = (A + B + C + D + E + F)/75 >= 75

but the question says that the average is equal to 75. Only way the equality holds if all the inequalities in (i) are equality

All 6 numbers are equal to 75

Sufficient

 

Similarly B can be shown sufficient