<p>I was going through Tip 13 in Dr. Chung's SAT Math book, and I came across a question that stumped me.</p>
<p>It is number 4 in the SAT Practice.</p>
<p>"A bag contains 8 white marbles, 8 blue marbles, 7 red marbles, and 6 yellow marbles. What is the least number of marbles that can be drawn from the bag, so that 3 of the same color marbles will be drawn?</p>
<p>A) 6
B) 9
C) 12
D) 13
E) 15</p>
<p>The answer turns out to be B, 9. Why is this though? It seems intuitive that the answer should be 3...but 3 is not an option.</p>
<p>We’re not talking about what’s possible. We’re talking about what makes it absolutely guaranteed that after x draws, we’ll have 3 of the same color marbles drawn. That’s 9. Because for example let’s say you draw 2 from Blue, then 2 from White, then 2 from Yellow, and then 2 from Red…you have drawn 8 marbles so far. Yet you want to have at least 3 marbles of the same color, and any marble you draw again, regardless of the bag, will be added to one of the other “2” stacks, making the same color marbles 3 of a kind.</p>
<p>Least number: 9</p>
<p>For more illustration (Let a marble drawn be denoted by an X):</p>
<p>You might want to do more examples – if 3 was intuitive, you’ll probably need more practice.</p>
<p>Another example:</p>
<p>A bag contains 8 white marbles, 8 blue marbles, 7 red marbles, and 6 yellow marbles. What is the least number of marbles that must be drawn from the bag, so that 3 blue marbles will be drawn?</p>
<p>This makes no sense can someone reexplain it. I can pick up 3 marbles in a bag right now full of 5,000,000 red marbles and 3 blue ones and have the 3 blue ones come up. That makes perfect sense to me. It’s logic on the SAT… so why do they go against their principals.</p>
<p>And on the other hand, I may pick 5,000,000 marbles before I pick a single blue one, so the only way to GUARANTEE that I get 3 of a color is to pick up every single marble.</p>
<p>I take my post back. I understand that it isn’t what is possible, but I don’t see a way of ensuring a possibility simply by taking the probability of the first 8 picks and then adding 1 </p>
<p>24 is the answer to your question though, trizzy?</p>
<p>I think the wording may be throwing you off – it isn’t saying what it means to say (assuming it’s transcribed correctly). As it is currrently worded, 3 is not just intuitive – it’s correct! The least number of marbles you can draw to get 3 of the same color is absolutely 3. But that’s not what it meant to ask. It meant: What is the fewest number of marbles you can draw to be CERTAIN of getting 3 of one color. Now 3 is not the answer any more, because though you MAY get 3 of one color, it is not certain. You could have bad luck and get different colors on each of your 1st 4 picks, then another one of each color on the next 4 picks. It would take bad luck to pick 8 and not get 3 of a kind, but if could happen. But the 9th pick would HAVE to make a trio of one color or another…</p>
<p>I wanted to point out that the current wording of the question makes it extremely confusing, but it seemed like many people had no problem understanding the question… I thought I was not able to comprehend a simple math question. I feel a bit more assured now… :)</p>
<p>On the real SAT, the problems will be worded with precision. You will be able to trust that things mean exactly what they say. Do NOT second-guess yourself or read into the problem things that aren’t there. (I’m no reading expert, but I think that may also apply to the reading section as well.)</p>