Is there other way to solve this question?

pckeller
Wed, 09 Nov 2011 13:57:32 +0000

As usual, I tried to do this by playing with numbers. And I sort of backed into an easy answer. Here goes:

First, I looked at 3 and 4 b/c they are in a 3:4 ratio. Then I thought, what would you have to add to each of them to make a 4:5 ratio? That’s easy – add 1 to each. But we are not adding one to each, we are adding 7 to each. So I took my original numbers and multiplied them by 7 (so that the proportional increase would be the same): now I have 21 and 28. And sure enough, if you increase them both by 7 you get 28 and 35 which is still a 4:5 ratio. So increase them by 14 each instead and you get 35 and 42 which are in a 5:6 ratio. So that’s the answer.

Then I realized that it was even easier: Notice that the second time, you are increasing them by another 7 each. In other words…

x ----> x+7 ----> x+7+7 = 3 ----> 4 ----> 5

y ----> y+7 ----> y+7+7 = 4 ----> 5 ----> 6

If the formatting of this post doesn’t get ruined, you may see what I meant…

Bottom line: if all that algebra you did is the only way to solve the problem then it is NOT a realistic SAT problem.