arithmetic mean:
sum of elements/number of elements
mode: the element that appears the most times in a set.
To find the value of k, use the arithmetic mean.
45 = 20 + 70 + 10 + k + 20 + 90/6
45 = 210 + k/6
45 × 6 = 210 + k
k = 270 – 210 = 60
With k = 60, rewrite the elements of the set in numerical order.
{10, 20, 20, 60, 70, 90}
The mode is 20, since it is the only element that appears more than once.
The correct answer is option (A).
Notice that the value of k is given as an answer option. A GRE trick is to offer an answer option that is a number from a previous step in finding the real answer. The median is also given as an answer option. Since the number of elements is even, the median is the mean of the 2 center elements: (20 + 60)/2 = 40.