The list of numbers $4, p, 8, q, 12$ has an arithm... | Free GMAT Practice Question | GMAT Panda

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The list of numbers 4, p, 8, q, 12 has an arithmetic mean of 8 . If p and q are integers and p is not equal to q, what is the median of the list?

Explanation	Calculations	Help
$We translate the question's "arithmetic mean of 8" into an equation relating the sum of the five numbers to their mean.$	$4 + p + 8 + q + 12 = 8 \times 5$
$We combine the known numbers to simplify the left side.$	$4 + 8 + 12 = 24$
$We substitute the simplified sum into the equation and simplify the right side.$	$24 + p + q = 40$
$We isolate the sum of p and q .$	$p + q = 16$
$Because p + q = 16 and p and q are distinct integers, one must be less than 8 and the other greater than 8, so in the sorted list the number 8 is in the middle.$	$8$

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C

The list of numbers 4, p, 8, q, 12 has an arithmetic mean of 8 . If p and q are integers and p is not equal to q, what is the median of the list?

Explanation	Calculations	Help
$We translate the question's "arithmetic mean of 8" into an equation relating the sum of the five numbers to their mean.$	$4 + p + 8 + q + 12 = 8 \times 5$
$We combine the known numbers to simplify the left side.$	$4 + 8 + 12 = 24$
$We substitute the simplified sum into the equation and simplify the right side.$	$24 + p + q = 40$
$We isolate the sum of p and q .$	$p + q = 16$
$Because p + q = 16 and p and q are distinct integers, one must be less than 8 and the other greater than 8, so in the sorted list the number 8 is in the middle.$	$8$

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C