<p>To be honest, I don’t really understand the answers for either questions, and I got 800 on the actual SAT (so don’t stress-- the second one at least is more difficult than the vast majority of SAT questions). I believe the first question to be a typo, unless they had an explanation that verifies 18 as the correct answer. </p>
<p>For the second question, the answer I got was 108. I’ll explain what I did, but perhaps some CC math whizzes can prove 101 as the right answer. This is how I did it:</p>
<p>There is a 5:6 ratio of red to white marbles and a 6:7 ratio of red to blue marbles. When I see the words “least possible number”, I immediately look for the lowest common multiple between 5 and 6. This number happens to be 30, so I mark this as the lowest possible amount of red marbles that satisfies the boundaries of the problem. </p>
<p>To keep the ratios constant for the blue and white marbles, I multiply the white marble number (the 6 in 5/6) by 6, and I multiply the blue marble number (the 7 in 6:7) by 6. I get 36 and 42, respectively. When I add 30+36+42, I get 108. I don’t know how they got 101, but if you have the explanation, I really would like to see it.</p>