GMATD11 wrote:
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.
Target question: How many of the numbers are equal to 75 ? Given: The average (arithmetic mean) of six numbers is 75 Statement 1: None of the six numbers is less than 75One possible scenario is that the 6 number are {75, 75, 75, 75, 75, 75}. This satisfies the conditions that none of the six numbers is less than 75, AND the average is 75
Notice that if we increase ANY of the 6 values, the resulting average will be greater than 75
So, it must be the case that the 6 number are {75, 75, 75, 75, 75, 75}.
The answer to the target question is
all 6 numbers are equal to 75Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: None of the six numbers is greater than 75.One possible scenario is that the 6 number are {75, 75, 75, 75, 75, 75}. This satisfies the conditions that none of the six numbers is greater than 75, AND the average is 75
Notice that if we decrease ANY of the 6 values, the resulting average will be less than 75
So, it must be the case that the 6 number are {75, 75, 75, 75, 75, 75}.
The answer to the target question is
all 6 numbers are equal to 75Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
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