The figure shown is folded to form a cube. Three faces meet at each corner. If the numbers on the three faces at a corner are multiplied, what is the largest possible product?
(A) 144
(D) 280
(B) 168
(E) 336
(C) 240
The figure shown is folded to form a cube. Three faces meet at each corner. If the numbers on the three faces at a corner are multiplied, what is the largest possible product?
(A) 144
(B) 168
(C) 240
(D) 280
(E) 336

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-472.jpg?height=326&width=252&top_left_y=875&top_left_x=1403)

Solution

When the figure is folded to make a cube, the numbers 8 and 6 are on opposite faces so that it is NOT possible to achieve $8 \times 7 \times 6$ or 336 . It is possible, however, to have the sides with 5,7 and 8 meet at a corner which gives the answer $5 \times 7 \times 8$ or 280 .

ANSWER: (D)