Problem Set #4

1) The question I've picked is # 17. It's about a number line. Marked on this number line with , are integers that come one after the other, but you can't actually see the numbers. There are four bigger dots (I've marked them with 0 s), and two of them are multiples of 3, and the other two are multiples of 5. What we're trying to find is the point that is a multiple of 15 (A,B,C,D, or E).

_,_0_0_,_,_,_,_,_,_,_0_,_0_,_,

               A BCDE

2) When I first looked at this question, it seemed pretty tricky to figure out. The written explanation just seemed to make it more complicated, so I decided to look really hard at the diagram. What struck me was that the 4 bigger circles - the ones that are multiples of 3 or 5 - were really close together. I realized that this number line had to be pretty small numbers, because the larger the multiples of 3 and 5, the farther apart they would be on the number line. That got me thinking. 

These _,_0_0_,_,_,_,_,_,_,_0_,_0_,_, couldn't both be multiples of 3 or both multiples of 5, and neither

                         A BCDE

could these , because they have to be at least 5 or 3 apart. So, I was looking for a two smaller numbers right next to eachother that were multiples of 3 and 5. Since they had to be small, I started from the bottom. 3 and 5, obviously not. They're not consecutive. 5 and 6 works, but that makes the second two 14 and 16, which aren't multiples of 3 or 5. Not 6 and 10, either, but 9 and 10 works! That would make the second pair 18 and 20, which fit perfectly on the number line and are multiples of 3 (18/6=3) and 5 (20/4=5)!

So it would look like this:

_8_9_10_11_12_13_14_15_16_17_18_19_20_21_22

                       A   B   C    D   E

So, which number is a multiple of 15? 

15!!!

So, the answer is D, 15.

3) The reason I like this question is because it requires a bit of logic - the fact that the numbers had to be smaller, because otherwise the multiples of 3 and 5 would be farther apart. Without that, it would have been immensely frustrating, because there are unlimited multiples of 3 and 5 - just not the ones we want.

4) What I have learned about problem solving through this question is to use all the information you're given. You can't just look at the written explanation, and you can't just look at the diagram. You have to use both, and a bit of mathematical reasoning, in order to solve the question. So, even if the written explanation is super complicated and you don't understand at all, use the diagram to help you understand, and it will start to make sense.