Math Question

<p>At a certain high school, there are 9 students on the math team and 10 students on the academic team. There are a total of 11 students who are on exactly one of the teams. Of those students who are on the math team, how many are also on the academic team?</p>

<p>Sorry I did not put the choices.
(A) 0
(B) 1
(C) 2
(D) 4
(E) 5</p>

<p>answer is D </p>

<p>no of students in both is x, in math only is y, in acad only is z
x+z=10 (1)
x+y=9 (2)
y+z=11 (3)</p>

<p>[(1)+(2)-(3)]/2 = x = 4</p>

<p>This can be done in a few seconds with the following single computation:</p>

<p>(19-11)/2 = 4.</p>

<p>See if you can figure out why this single computation works. If not, let me know and I will provide further explanation.</p>

<p>Hint: Draw a Venn Diagram, or use the basic formula Total = A + B - Both</p>

<p>Why are we dividing by 2?</p>

<p>The total of 19 contains the students that are on both teams TWICE. When we subtract 11 we are only subtracting the students that are on one team or the other. So we are left with twice the students that are on both teams.</p>

<p>Thanks for reply :)</p>

<p>I got it. Thank you very much!</p>