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16 Sep 2014, 01:08
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If the average (arithmetic mean) of four positive integers is 30, how many of these four integers are greater than 20?
(1) One of the integers is 98
(2) The median of the four integers is less than 12
(1) One of the integers is 98
(2) The median of the four integers is less than 12
16 Sep 2014, 01:08
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Official Solution:
If the average (arithmetic mean) of four positive integers is 30, how many of these four integers are greater than 20?
The average of the four positive integers is 30, which means that the sum of these four positive integers is \(4*30=120\).
(1) One of the integers is 98.
If one of the integers is 98, then the sum of the other three is \(120-98=22\). Since all the integers are positive, none of these three remaining integers can be greater than 20 (the largest possible value for one of them is 20, if the other two are both 1). Therefore, there is only one integer greater than 20, which is 98. Sufficient.
(2) The median of the four integers is less than 12.
If the set is \(\{1, 1, 1, 117 \}\), then there is only one integer greater than 20. However, if the set is \(\{1, 1, 21, 97 \}\), then there are two integers greater than 20. Not sufficient.
Answer: A
If the average (arithmetic mean) of four positive integers is 30, how many of these four integers are greater than 20?
The average of the four positive integers is 30, which means that the sum of these four positive integers is \(4*30=120\).
(1) One of the integers is 98.
If one of the integers is 98, then the sum of the other three is \(120-98=22\). Since all the integers are positive, none of these three remaining integers can be greater than 20 (the largest possible value for one of them is 20, if the other two are both 1). Therefore, there is only one integer greater than 20, which is 98. Sufficient.
(2) The median of the four integers is less than 12.
If the set is \(\{1, 1, 1, 117 \}\), then there is only one integer greater than 20. However, if the set is \(\{1, 1, 21, 97 \}\), then there are two integers greater than 20. Not sufficient.
Answer: A
General Discussion
18 Jan 2018, 22:38
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Please explain:-
There are many ways to get a2+a3+a4=22 ,and it may or may not require one of the number to be 20, so 20 can be used 0 time or 1 time...so statement 1 is not sufficient...
There are many ways to get a2+a3+a4=22 ,and it may or may not require one of the number to be 20, so 20 can be used 0 time or 1 time...so statement 1 is not sufficient...
