<p>there is always an SAT question where I always get wrong where it is like (blah means any number):</p>
<p>there is a blah number of students in a school. Blah number play guitar, blah number play both guitar and piano. How many number of students play piano alone?</p>
<p>something like that.</p>
<p>Do you use venn diagram? alegbraically?</p>
<p>here is a real question:</p>
<p>After polling a class of 20 music students by a show of hands, you find that 8 students play the guitar and 9 students play the piano, what is the minimum number of students in this music class who can play both guitar and piano</p>
<p>A class of 29 students sponsored two field trips: one to a zoo and one to musuem. Every studen attended at elsat one of the field trips, and 10 students attended both. If twice as many students went to the zoo as went to the museum, how many students went to the zoo?</p>
<p>I usually use algebra. It might help to draw a Venn diagram, then let each of the sections be A,B, and C. Then set up 3 equations with the variables and solve.</p>
<p>After polling a class of 20 music students by a show of hands, you find that 8 students play the guitar and 9 students play the piano, what is the minimum number of students in this music class who can play both guitar and piano</p>
<p>since the answer choices are not here T_T
my guess would be 8?</p>
<p>10 of the students went to both the zoo and the museum. So there were 29 + 10 = 39 attendees (think of it as how many tickets were purchased). If there were twice as many tickets to the zoo as to the museum then</p>
<p>3x = 39
x = 13
2x =26</p>
<p>The music one does not seem to make sense. If only 8 students can play the guitar then the maximum number of students that can play the guitar and the piano is 8. There is not enough information to say what the minimum is. Logically the minimum could be 0 students that can play both.</p>
<p>i think i misread the first, can u make it more clear?</p>
<p>anyway
2.
Z=2M
so 2M + M - 10 = 29
because the 10 includes both z and m, so there’s 10 extra. u know wat i mean? they’re the same 10 that make up that number.
so 3M=39
M=13
Z=26</p>
<p>edit: swimcatsmom, yes thats true, the mini can be 0,so something’s wrong with the question.</p>
<p>Im a bit lost on the first one, but the second ones easy</p>
<p>We’re told that 10 kids went to both the zoo and the Museum, but we dont know how many went to the zoo or museum. Lets say the number of students who went to the museum as M and Zoo as Z ,</p>
<p>However, M and Z includes the 10 kids that attended both. To find only those who went to the zoo and museum, we subtract 10 from both Z and M</p>
<p>we get</p>
<p>Z-10 and M-10 </p>
<p>since the total student count is 29, we must add all 3 groups. Those that went to the museum only, the zoo, and both.</p>
<p>so you add all 3</p>
<p>Z-10 + M-10 + 10 </p>
<p>But hey, we’re told that twice as many kids went to the zoo then the museum. So we can express that as 2m=Z</p>
<p>Substitutue it into the previous equation.</p>
<p>2m-10 + m - 10 + 10 = 3M-20<br>
3m-20=29
Solve for M</p>
<p>M = 13. </p>
<p>Now we know the number of kids who went to the museum, which is 13. However, we want the number of kdis who went to the zoo. And twice as many kids went to the zoo according to the Q.</p>
<p>U means union
A U B means total number of people
A means total number of people who satisfy A
B means total number of people who satisfy B
A intersection B means number of people who satisfy both A and B simultaneously.</p>
<p>I dug out my daughter’s old ACT prep books (actually they are sitting on the fireplace waiting to be donated to the high school) and the answer in her book to that question was answer F - 0.</p>
<p>Her book was copyright 2005. maybe yours has a typo.</p>
<p>Yup. The answer is 0.
Because the total number of student playing guitar and piano is 8+9=17, which does not exceed the total number of students ‘20’. Therefore, the minimum number of students in this music class who can play both guitar and piano is 0.</p>
<p>Q1) After polling a class of 20 music students by a show of hands, you find that 8 students play the guitar and 9 students play the piano, what is the minimum number of students in this music class who can play both guitar and piano?</p>
<p>A U B = A + B - (A int. B)
A U B = 8 + 9 - (students who play both)</p>
<p>Now 20 music students is the universal set, out of which A (guitar) and B (piano) have been taken… There can also be students who don’t play any of these.</p>
<p>So
A U B = Universal set - students who belong in neither
A U B = 20 - some number
so max value of A U B = 20</p>
<p>and
so
A U B = 8 + 9 - (students who play both)
20 = 8 + 9 - (students who play both)
so students who play both has to be zero… (minimum possible number) and at this situation, the number of students who play neither instrument is 3.</p>
<hr>
<p>Q2) A class of 29 students sponsored two field trips: one to a zoo and one to museum. Every student attended at least one of the field trips, and 10 students attended both. If twice as many students went to the zoo as went to the museum, how many students went to the zoo?</p>
<p>Here ‘Every student attended at least one of the field trips’ implies that the union of all the given sets is itself the Universal Set, unlike in the previous question.</p>
<p>Z U M = Z + M - ( Z int. M)
29 = Z + M - (10)
39 = Z + M
(Now, given that 2M = Z or M = Z/2)
39 = Z + Z/2
39 = 3Z/2
Z = 26 students</p>
<p>Quix,
the first question is kinda different like the normal this type of questions. Usually, in the normal questions, A + B is greater than A U B, just like the second question. And you could simply determine (A intersection B) by A+B - (A U B).
However, in the first one, A + B is less than A U B, which means A + B cannot make up the 20-student music class, which further means A might not intersect with B at all. That leads you to the answer 0.
A + B - (A intersection B) = A U B , well, if you still want to use this formula to explain the problem.
A + B = 8 + 9 =17.<br>
A U B = 20
17 - (A int. B) = 20
(A int. B)= -3 … How could -3 people exist?
Therefore, the answer is simply 0.</p>