<ol>
<li><p>In a certain high school, there are three times as many band members as orchestra members and twice as many orchestra members as jazz choir members. If no student can be enrolled in more than one of the three activities and there are 108 members in the three activities, how many students are in band? </p></li>
<li><p>For their graduation ceremony, the 100 students in Arlenes senior class were each assigned a different whole number from 1 to 100. Arlene and her classmates entered the auditorium in numerical order, and every 20 students filled a different row, maintaining that order. There were aisles on both ends of each row, and only one student sat between Arlene and the aisle. Which of the following cannot be Arlenes number? A) 19 B) 42 C) 59 D) 69 E) 82</p></li>
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<p>Thanks!</p>
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<li>Let x be the number of jazz choir members. Therefore, number of orchestra members is 2x, and number of band members is 6x. So x+2x+6x=108
9x=108
x=12
Then multiply by 6 since you’re trying to find 6x.
The answer is 72.</li>
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<ol>
<li>D</li>
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<p>If there are 20 on each row, then the rows are like this:</p>
<p>1-20
21-40
41-60
61-80
81-100</p>
<p>If she was number 69, then she would be in the middle of a row, not within one seat of an aisle. </p>
<p>Hope this helped!</p>
<p>Post #2. Why 2x? </p>
<p>Here is my reasoning:</p>
<p>Band: x
Orchestra: 3x
Jazz: 6x
x+3x+6x=108
x=10.8 Obviously there can’t be 10.8 students!!! absurd. What am I doing wrong?</p>
<p>I think you’re doing it backward. It’s twice as many orchestra as jazz and three times as many band as orchestra. So: </p>
<p>Jazz = x
Orch. = 2x (twice as many as band)
Band = 6x (triple what orch. has)</p>
<p>Yeah! I got it now. But I still don’t understand why we should use reverse method.</p>
<p>It’s just the way that the question is written. They’re trying to trip people up.</p>
<p>aha! Thank you so much!</p>