Step-by-step explanation:There’s two ways of looking at this problem, a simple way and a complicated way. Both will get you 12. I’ll start with the simple way:
3 + 1 = 4
4 + 2 = 6
6 + 1 = 7
7 + 2 = 9
9 + 1 = 10
10 + 2 = 12
simple, right? +1, +2, and so on forever…
Now for the more complicated approach
look at every other number for a pattern.
3 + 3 = 6
6 + 3 = 9
9 + 3 = 12
Boom.
Now I know what you’re thinking, why would you skip half the numbers when looking for a pattern? When I analyze problems like these they usually aren’t as simple as +1 + 2. Sometimes the patterns aren’t so easy to see. Sometimes the pattern is only every other number and the rest are random nonsense numbers. The reason I added the second method is to encourage critical thinking in problems like these. In my college algebra class we had a test with a bonus question that looked something like this:
7 and 5 = 12235
8 and 4 = 12448
9 and 3 = 12627
9 and 4 = _______
To me it was clear that the answer was 13536 after about 30 seconds but I later found out that I was the ONLY student to answer this question correctly. I was in awe. The issue was not in knowledge, all you need to know to solve this problem is simple addition, subtraction, and multiplication skills. The issue was not experience. I’ve never seen a problem like this before in my life. So why was I the only person to get this right? First of all, I didn’t give up. Second of all, I thought about it objectively. If you saw those numbers as 12,235, 12,448, and 12,627 then you would never figure it out. It dawned on me while looking at the first problem ending in 35, knowing that 5 x 7 = 35 and thinking “that can’t be a coincidence”. The first two numbers are the numbers added together: 9 + 4 = 13. The next number is the numbers subtracted: 9 - 4 = 5. The next number is the numbers multiplied: 9 x 4 = 36. Put them together and you have 13536. Now once again I know what you’re thinking, did this person really just spend over 30 minutes of his life ranting about math to tell me that the answer is 12? Yes. Yes I did.