<li>If n distinct planes intersect in a line, and another line l intersects one of these planes in a single point, what is the least number of these n planes that l could intersect?</li>
</ol>
<p>A) n
B) n-1 - Correct answer
C) n-2
D) n/2
E) (n-1)/2</p>
<li>The radius of the base of a right circular cone is 6 and the radius of a parallel cross section is 4. If the distance between the base and the cross section is 8, what is the height of the cone?</li>
</ol>
<p>A) 11
B) 40/3
C) 16
D) 20
E) 24 - Correct answer</p>
<li>In how many ways can 10 people be divided into two groups, one with 7 people and the other with 3 people?</li>
</ol>
<p>A) 120 - Correct answer
B) 210
C) 240
D) 5,040
E) 14,400</p>
<ol>
<li>Ok in the first one, all of the planes must intersect to form a line, so they must be arranged in a star like pattern all with a center axis. Another line that hits a plane once will intersect all of the other planes except the one that is parallel to it, making the answer n-1.</li>
</ol>
<p>2
.</p>
<p>_ _</p>
<hr>
<hr>
<p>This is the shape of the triangle that makes the cone. For each decrease of 2 in the the base of the cone, the height increases by 8. So, if the base is 6 long, 6/2 = 3, and 3*8 is 24.</p>
<ol>
<li>You have ten, order doesn't matter, and you're choosing three or seven, so you do 10 nCr 3, which equals 120. So does 10 nCr 7.</li>
</ol>
<p>Or if you prefer working with proportions, here's a different way to do #2:</p>
<p>h is the height of the whole cone, and h-8 is the height of just the top part. 6 is the rad. of the whole thing, and 4 is the radius of the top part. So:</p>