Oranges are placed in a pyramid-like stack with each layer completely filled. The base is a rectangle that is 5 oranges wide and 7 oranges long. Each orange, above the first layer, rests in a pocket formed by four oranges in the layer below, as shown. The last layer is a single row of oranges. The total number of oranges in the stack is
(A) 53
(B) 80
(C) 82
(D) 85
(E) 105

![](https://cdn.mathpix.com/cropped/2024_04_20_ac36362783317e0251fdg-069.jpg?height=220&width=285&top_left_y=2102&top_left_x=1343)
Because of the way in which the oranges are stacked, each layer is a rectangle whose length is 1 orange less and whose width is 1 orange less than the layer below.

The bottom layer is 5 by 7 and so contains 35 oranges.

The next layer is 4 by 6 and so contains 24 oranges.

The next layer is 3 by 5 and so contains 15 oranges.

The next layer is 2 by 4 and so contains 8 oranges.

The next layer is 1 by 3 and so contains 3 oranges. This is the last layer, as it consists of a single row of oranges.

The total number of oranges in the stack is thus $35+24+15+8+3=85$.

ANSWER: (D)