Numbers on a cube

Question

Lin has a cube. On each side of the cube, she writes a different positive number.

The numbers on opposite sides of Lin's cube are consecutive.

Which of the following is a possible sum of the six numbers on Lin's cube?

(A) 36

(B) 31

(C) 22

(D) 19

Answer 1

The problem should probably state that positive integers are written on the faces of the cube.

Picture looking at the cube from the front, so the sides can be thought of at top-bottom, left-right, and front-back.

Answer 2

6 sides 3 pairs

1 and 2

3 and 4

5 and 6

sum of 1 through 6= 3+7+11 = 21

1+2+3+4+5+6= 21

31 might be a typo and was supposed to be 21, so might choose B)

but the instructions often read choose the "best" answer, and 22 is closest to 21, and it also might be a typo, hitting the 2 when 1 was intended for the unit digit. C) has 2 things going for it: possible type and the "best" answer as is, just off by 1, closer than any of the other options

A) is the worst option. D) 2nd worst, only off by 2 from 21

any pair of consecutive integers sums to an odd number

3 pairs will also sum to an odd number

that narrow it down to 19 and 31 as the only possibilities

2 and 3

2 and 3

4 and 5

sum to 19

6 and 7

5 and 6

3 and 4

sum to 31

so go with B) and D), if you are allowed integers beyond 1 to 6 or repetitions