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26 May 2017, 04:43
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If the average (arithmetic mean) of 5 integers is 6, what is the standard deviation of the integers?
(1) None of the 5 integers are greater than 6
(2) None of the 5 integers are less than 6
(1) None of the 5 integers are greater than 6
(2) None of the 5 integers are less than 6
26 May 2017, 04:45
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Official Solution:
This question is the most common type of question in GMAT math. You must use the fact that if range=Max-min=0, mean=Maximum, or mean=minimum, then all elements have the same value, and then you can get standard deviation (d) = 0.
In the original condition, there are 5 variables (5 integers) and 1 equation (mean=6). In order to match the number of variables to the number of equations, there must be 4 equations. Therefore, E is most likely to be the answer. By solving con 1) and con 2):
In the case of con 1), you get no greater than= at most = Maximum, and from Maximum=6=mean, you get standard deviation (d) = 0, hence it is unique and sufficient.
In the case of con 2), you get no less than= at least = minimum, and from minimum=6=mean, you get standard deviation (d) = 0, hence it is unique and sufficient. Con 1) = con 2), and therefore D is the answer.
Answer: D
This question is the most common type of question in GMAT math. You must use the fact that if range=Max-min=0, mean=Maximum, or mean=minimum, then all elements have the same value, and then you can get standard deviation (d) = 0.
In the original condition, there are 5 variables (5 integers) and 1 equation (mean=6). In order to match the number of variables to the number of equations, there must be 4 equations. Therefore, E is most likely to be the answer. By solving con 1) and con 2):
In the case of con 1), you get no greater than= at most = Maximum, and from Maximum=6=mean, you get standard deviation (d) = 0, hence it is unique and sufficient.
In the case of con 2), you get no less than= at least = minimum, and from minimum=6=mean, you get standard deviation (d) = 0, hence it is unique and sufficient. Con 1) = con 2), and therefore D is the answer.
Answer: D
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