how to understand the verbage of SAT math problem

<p>Here is a math problem from the collegeboard online SAT prep:</p>

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<h2>In an art class, there were just enough staplers, rulers and glue bottles so that every 2 students had to share a stapler, every 3 students had to share a ruler, and every 4 students had to share a glue bottle. If the sum of the number of staplers, rulers, and glue bottles used by the class was 65 how many students were in the class?</h2>

<p>It is very easy to compute the answer if we realize that every student is using all three - stapler, ruler and glue bottle. Is it "had to share" or "used by the class" that indicates every student is using all three? I guess I am trying to understand how to understand the verbage when similar questions are asked. Any suggestions?</p>

<p>I think it’s “there was just enough” and “had to share.” This question is confusing, though. I had to read it a couple times to understand what it’s trying to say. It annoys me that CB tries to throw you off with their wording in a math problem, but hey, that’s the SAT.</p>

<p>It is saying that there are only enough supplies to go around if the students share. Therefore there are fewer of each supply than there are students. The first thing you know is that it must be a multiple of 2,3 and 4. Take the smallest common multiple of those three numbers which is 12. In a class of 12 there will be 6 staplers (2 students sharing a stapler), 4 rulers and 3 glue bottles. Add those up and you get 13 supplies for 12 students. Now, divide 65 by 13, you get 5. So now just multiply the number of students, 12, by the number you just determined, 5. (12)(5)=60</p>

<p>For every two students you have one stapler. So if there are x students, there will be x/2 staplers, x/3 rulers, x/4 glue bottles (integer values).</p>

<p>Hence x/2 + x/3 + x/4 = 65, solving yields x = 60.</p>

<p>I always have trouble with these.</p>