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 GMAT 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.