Different whole numbers are written on the face of a cube, one number on each face.
The sum of the two whole numbers on any pair of opposite faces of the cube is the same.
The face opposite to 18 has a prime number, A.
The face opposite to 14 has a prime number B.
And, the face opposite to 35 has a prime number C.
What is A + B + C?
Answers
Answer:
The numbers on the faces of this cube are consecutive whole numbers. The sums of the two numbers on each of the three pairs of opposite faces are equal. The sum of the six numbers on this cube is
[asy] draw((0,0)--(3,0)--(3,3)--(0,3)--cycle); draw((3,0)--(5,2)--(5,5)--(2,5)--(0,3)); draw((3,3)--(5,5)); label("$15$",(1.5,1.2),N); label("$11$",(4,2.3),N); label("$14$",(2.5,3.7),N); [/asy]
$\text{(A)}\ 75 \qquad \text{(B)}\ 76 \qquad \text{(C)}\ 78 \qquad \text{(D)}\ 80 \qquad \text{(E)}\ 81$
Solution
The only possibilities for the numbers are $11,12,13,14,15,16$ and $10,11,12,13,14,15$.
In the second case, the common sum would be $(10+11+12+13+14+15)/3=25$, so $11$ must be paired with $14$, which it isn't.
Thus, the only possibility is the first case and the sum of the six numbers is $81\rightarrow \boxed{\text{E}}$
Answer:
The numbers on the faces of this cube are consecutive whole numbers. The sums of the two numbers on each of the three pairs of opposite faces are equal. The sum of the six numbers on this cube is
[asy] draw((0,0)--(3,0)--(3,3)--(0,3)--cycle); draw((3,0)--(5,2)--(5,5)--(2,5)--(0,3)); draw((3,3)--(5,5)); label("$15$",(1.5,1.2),N); label("$11$",(4,2.3),N); label("$14$",(2.5,3.7),N); [/asy]
$\text{(A)}\ 75 \qquad \text{(B)}\ 76 \qquad \text{(C)}\ 78 \qquad \text{(D)}\ 80 \qquad \text{(E)}\ 81$
Solution
The only possibilities for the numbers are $11,12,13,14,15,16$ and $10,11,12,13,14,15$.
In the second case, the common sum would be $(10+11+12+13+14+15)/3=25$, so $11$ must be paired with $14$, which it isn't.
Thus, the only possibility is the first case and the sum of the six numbers is $81\rightarrow \boxed{\text{E}}$
Step-by-step explanation: