What am I missing?

Question

This problem doesn't seem solvable to me.

 

Given the following points, predict the missing number. (3,8) (6,6) (7,8) (9,12) (12, ?)

 

Choices: 6, 3, 7, 9, 12

Answer 1

(3,8) and (6,6) connect to form a straight line(obviously !) Then...

(6,6), (7,8), and (9,12) are all on the same straight line whose equation is y=2x-6.

I found the slope (rise/run) first and then the y-intercept (b).

The point (12,18) is on this line also but 18 is not one of the choices for y.

Maybe 18 was left out of the choices.

Another possibility is the following...

each odd x is paired with an even y and the even x is

paired with itself, therefore 12 would be paired with 12, which is one of the choices

 

Answer 2

Hi Dulcie,

 

I've been staring at these numbers for quite a while, trying all sorts of combinations ..., and there is just one pattern that I can see. It's a long shot, but it's the only one I see --

 

take the product of the (x,y) for each pair --

 

  (3,8) -- 3 * 8 = 24

  (6,6) -- 6 * 6 = 36

  (7,8) -- 7 * 8 = 56

  (9,12) -- 9 * 12 = 108

 

The pattern is simply that x_i * y_i keeps INCREASING.

 

Given that the next x is 12, then of the y-choices (6, 3, 7, 9, 12) only one value when multiplied by x=12 will be greater than 108.

 

I'll let you finish.

 

Best wishes.

 

ps. I say it's a long shot, but it is a correct answer. There may be other patterns, and thus other solutions, but this is a solution.