3, k, 2, 8, m, 3 The arithmetic mean of the list of numbers above is 4 . If k and m...

Question

3, k, 2, 8, m, 3 The arithmetic mean of the list of numbers above is 4 . If k and m are integers and k is not equalt to m what is the median of the list?

GMAT Panda · Accepted Answer

3 (C) Write the equation relating the arithmetic mean to the sum of the six numbers. 3 + k + 2 + 8 + m + 3 = 4 6 Simplify each side of the equation. 16 + k + m = 24 Isolate the sum of k and m. k + m = 8 Since k and m are distinct integers whose sum is 8, one must be less than 4 and the other greater than 4. (k,m) < 4 < (k,m) When the six numbers are arranged in ascending order, the two original 3's occupy the third and fourth positions. (k,m), 2, 3, 3, (k,m), 8 Since we have an even number of values, the median is the average of the two middle values (third and fourth numbers in the ordered list). 3 + 3/2 = 3

Explanation	Calculations	Help
$Write the equation relating the arithmetic mean to the sum of the six numbers.$	$3 + k + 2 + 8 + m + 3 = 4 \times 6$
$Simplify each side of the equation.$	$16 + k + m = 24$
$Isolate the sum of k and m .$	$k + m = 8$
$Since k and m are distinct integers whose sum is 8, one must be less than 4 and the other greater than 4.$	$min (k, m) < 4 < max (k, m)$
$When the six numbers are arranged in ascending order, the two original 3's occupy the third and fourth positions.$	${min (k, m), 2, 3, 3, max (k, m), 8}$
$Since we have an even number of values, the median is the average of the two middle values (third and fourth numbers in the ordered list).$	$\frac{3 + 3}{2} = 3$

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