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12 May 2021, 19:00
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
54% (01:32) correct
46%
(01:35)
wrong
based on 170
sessions
History
Date
Time
Result
Not Attempted Yet
What is the median of the numbers 4, 5, 6, 7, 9, and x?
(1) x > 7
(2) The mean of the six numbers is equal to their median.
(1) x > 7
(2) The mean of the six numbers is equal to their median.
16 May 2021, 02:30
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Bunuel
What is the median of the numbers 4, 5, 6, 7, 9, and x?
The median of a set with even number of terms is the average of two middle terms when arranged in ascending/descending order.
(1) x > 7 --> two middle terms are 6 and 7, thus median=(6+7)/2=6.5. Sufficient.
(2) The mean of the six numbers is equal to their median.
If \(x\leq{5}\), then two middle terms are 5 and 6, thus median=(5+6)/2=5.5. In this case mean=(4+5+6+7+9+x)/6=5.5 --> x=2. Possible scenario.
If \(x\geq{7}\), then two middle terms are 6 and 7, thus median=(6+7)/2=6.5. In this case mean=(4+5+6+7+9+x)/6=6.5 --> x=8. Possible scenario.
Not sufficient.
Answer: A.
P.S. For (2): if \(5<x<7\), then two middle terms are x and 6, thus median=(x+6)/2. In this case mean=median=(4+5+6+7+9+x)/6=(x+6)/2 --> x=6.5. Also, possible scenario.
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Hope it helps.
General Discussion
12 May 2021, 21:44
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Bunuel
Median of 4, 5, 6, 7, 9 and x =?
Statement 1:
x > 7
If x > 7, then 6 and 7 are the two middle terms in ascending order.
Median = Average of 6 and 7 = 6.5
Statement 1 is Sufficient.
Statement 2:
Mean = Median
If x = 2, then Mean = Median = 5.5
If x = 8, then Mean = Median = 6.5
Statement 2 is Not Sufficient.
So, correct answer is option A.
