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16 Jan 2023, 02:30
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The mean of 63, 66, 69, x and 75 is equal to the median of the set. What is the value of x?
(1) The average of x and 75 is the same as the average of 63 and 69.
(2) x is smaller than 75.
(1) The average of x and 75 is the same as the average of 63 and 69.
(2) x is smaller than 75.
16 Jan 2023, 13:12
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Bunuel
Statement 1
(1) The average of x and 75 is the same as the average of 63 and 69.
\(\frac{x + 75 }{ 2} = \frac{63 + 69 }{ 2}\)
We can find an unique value of x, hence sufficient.
Statement 2
x is smaller than 75.
As the number of terms is odd, the median of the set must be the member of the set. Hence we can fix any number as median and adjust the value of x accordingly so that the value of mean equals to the value of the median.
The statement is not sufficient as we will not get an unique value of x.
Option A
16 Jan 2023, 14:40
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Bunuel
Rule:
For any set that is SYMMETRICAL ABOUT THE MEDIAN, average = median.
Here, the given set will be symmetrical about the median in the following cases:
Case 1 --> x=57, 63, 66, 69, 75
Case 2 --> 63, 66, 69, x=72, 75
Note the following:
In each case, average of the blue pair = average of the red pair = median.
Statment 1:
Here, only Case 1 is viable, implying that x=57.
SUFFICIENT.
Statement 2:
Here, both Case 1 and Case 2 are viable.
In Case 1, x=57.
In Case 2, x=72.
Since x can be different values, INSUFFICIENT.
For a similar problem in the OG22, click here.
