Question

Five points are located on a line. When the ten distances between pairs of points are listed from smallest to largest, the list reads: 2, 4, 5, 7, 8, k, 13, 15, 17, 19. What is the value of k

Answer 1

k = 12

Explanation:

To find the missing number, we would first draw the number line and insert some of the numbers listed above using trial and error.

The numbers would be from 0 to 19. This is because the ten numbers given are the distances between pairs of points from smallest to largest.

That is to get 2, the pairs of point would have to be between 0 and 2, likewise to get 19, the pairs of point would have to be between 0 and 19.

Let's draw the first number line by placing the numbers from the above analysis: 0, 2 and 19

To get a distance of 7, the pairs could be 0 and 7 ; 8 and 15

We would represent this on the number line.

From the arrows drawn, we can see we have distances: 2, 7, 15, 19, 5, 13, 17, 8, 12, 4

The number available in this list but not specified in the ten distance list in the question is 12.

Therefore, the value of k = 12