Question number 26. The numbers 3, 4, 5, 6, and 7 are to be placed in the 5 circles of the figure so that the number inside each triangle is the product of the 3 numbers on its vertices. What is the sum of the 3 numbers on the vertices of the colored triangles? So looking at these 4 numbers, what we can see immediately that they all have in common is that they're all divisible by 7. So if they're all divisible by 7, then that means that 7 has to be the number in the center. Then we see that the 2 numbers on the left are divisible by 5. 105 and 210 are both quite obviously divisible by 5, so we can put a 5 over here in this left vertex. Now that we have 2 numbers and we have this product, we can easily figure out the third factor for the bottom vertex and the top vertex. The top vertex will be 3, and the bottom vertex will be 6. Of course that only leaves one number left, which is 4 for the right vertex. So that gives us 7, 4, and 6 as the values for the vertices of the colored triangle. 7 plus 4 plus 6 is equal to 17, so our final answer is D.

triangle vertices

number placement

product calculation

divisibility

sum of vertices