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07 Sep 2022, 06:28
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E
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53%
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{2, 4, 8, 10, 12, x}
What is the value of x in the data set shown above ?
(1) The median and the average (arithmetic mean) of the data set are equal.
(2) x < 16.
What is the value of x in the data set shown above ?
(1) The median and the average (arithmetic mean) of the data set are equal.
(2) x < 16.
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10 Sep 2022, 13:37
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Bunuel
Statement 1
The median and the average (arithmetic mean) of the data set are equal.
Case 1
The easiest way we can make the mean and the median equal is by assuming a value of x such the series is in Arithmetic Progression.
If x = 6
2 4 6 8 10 12
The median of the set = 7 and the mean = 7
In this case x = 6
Case 2
However, we can first obtain a mean and then assume the value of x to fit in the criteria.
Ex. Let the median be equal to \(\frac{4 + 8 }{ 2}\) = 6
Based on this mean , x = 0
0 2 4 8 10 12
As we have obtained multiple values of x, this statement is not sufficient.
Statement 2
x < 16
Doesn't provide any information as there can infinite values under 16. Hence not sufficient
Combination
Combining both the information does not help either as both 0 and 6 from case 1 and case 2 are possible.
Option E
08 Nov 2024, 04:10
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