If the average (arithmetic mean) of the five numbers \(x, 7, 2, 16\) and \(11\) is equal to the median of five numbers, what is the value of \(x.\)
(1) \(7 < x < 11.\)
(2) \(x\) is the median of the five numbers.
Answer: D
Source: GMAT Prep
If the average (arithmetic mean) of the five numbers \(x, 7, 2, 16\) and \(11\) is equal to the median of five numbers,
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The numbers are x, 7, 2, 16, 11
$$\frac{x+7+2+16+11}{5}=median$$
Target question: what is the value of x?
Statement 1: 7 < x < 11
The possible values of x include 8, 9 and 10
Order of set => 2, 7, x, 11, 16. Irrespective of the value of x, it will still be the median.
$$Therefore,\ \frac{x+7+2+16+11}{5}=x$$
x + 36 = 5x
4x = 36
x = 36/4 = 9
Statement 1 is SUFFICIENT.
Statement 2: x is the median of the 5 numbers
$$\frac{2+7+x+11+16}{5}=x$$
This is the same as statement 1 above; hence, x = 9. Therefore, statement 2 is SUFFICIENT.
Since each statement is SUFFICIENT alone, the correct answer is option D
$$\frac{x+7+2+16+11}{5}=median$$
Target question: what is the value of x?
Statement 1: 7 < x < 11
The possible values of x include 8, 9 and 10
Order of set => 2, 7, x, 11, 16. Irrespective of the value of x, it will still be the median.
$$Therefore,\ \frac{x+7+2+16+11}{5}=x$$
x + 36 = 5x
4x = 36
x = 36/4 = 9
Statement 1 is SUFFICIENT.
Statement 2: x is the median of the 5 numbers
$$\frac{2+7+x+11+16}{5}=x$$
This is the same as statement 1 above; hence, x = 9. Therefore, statement 2 is SUFFICIENT.
Since each statement is SUFFICIENT alone, the correct answer is option D