<p>As usual, I tried to do this by playing with numbers. And I sort of backed into an easy answer. Here goes:</p>
<p>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.</p>
<p>Then I realized that it was even easier: Notice that the second time, you are increasing them by another 7 each. In other words…</p>
<p>Thanks for the answer it made perfect sense,but in the SAT day I sometimes get frustrated about which way to solve it and end up losing some time.</p>