MATH IIC questions...Candy for you if you answer

Discus: SAT/ACT Tests and Test Preparation: October 2003 Archive: MATH IIC questions...Candy for you if you answer
 By Sandy (Sandy) on Tuesday, October 07, 2003 - 06:58 pm: Edit

Hey guys,

1) If P and Q are different points in a plane, the set of all points in this plane that are closer to P than to Q is:
a)the region of the plane on one side of a line
b) the interior of a square
c) a wedge-shaped region of the plane
d) the region of the plane bounded by a parabola
e) the interior of a circle

I am not visualizing this problem. Please explain.

2) 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?
a) n
b) n-1
c) n-2
d) n/2
e)(n-1)/2

3) In how many ways can 10 people be divided into two groups, one with 7 people and the other with 3 people?
a) 120
b) 210
c) 240
d) 5040
e) 14400

Guys, I know the answers to these questions. I just don't know how to get to them. I know what to do , but that does not lead to the correct answers. I need explanations. Thank you for your help.
Oh, ya, pick up your candy tomorrow!

 By Sandy (Sandy) on Tuesday, October 07, 2003 - 07:32 pm: Edit

bump

 By Freak4korn72 (Freak4korn72) on Tuesday, October 07, 2003 - 08:52 pm: Edit

I'll take a stab at number one and say its A.

The only thing I could say to do for that one is draw it on a graph and put two points kind of far from each other and draw a perpendicular line half way between them (if PQ was a line segment). You can pick any point in the region of P and it will always be closer to P than it is to Q (with exception to those that are on the line which would be same distance.. I think)..

 By Wrathofgod64 (Wrathofgod64) on Tuesday, October 07, 2003 - 09:16 pm: Edit

I think # 3 is A. the reason is because u use 10 C 7 or 10 C 3 which is the same thing. First thing ignore the last part of the question where it says "and the other with 3 people". Cuz if u arrange one group of 7 people, the other group will automatically have 3 people cuz there are 10 people in total. Now think we have 10 people and how many ways can u pick 7 of them at a time. Let's simplify this problem and say there are 4 people and u wanna split these 4 people into 2 groups of 2. the four people are A, B, C, and D. How many ways can u choose 2? AB, AC, AD, BC, BD, CD, therefore 6 ways. Similarly there are 120 ways u can choose 7 people out of a total of 10 people. hope this helps.

 By Bigman82085 (Bigman82085) on Tuesday, October 07, 2003 - 10:47 pm: Edit

#2 is B from my understanding. From the planes that intersect to the line, only one can run parallel to the line. Thus, this is the only one that will not intersect the line. So, the answer is n-1.

 By Sandy (Sandy) on Wednesday, October 08, 2003 - 03:05 pm: Edit

You guys are all correct. Good job! I understand them now.

 By Becks777 (Becks777) on Wednesday, October 08, 2003 - 06:57 pm: Edit

btw sandy.....what number are these questions.do they come in the end, begining..........?

 By Sandy (Sandy) on Wednesday, October 08, 2003 - 07:58 pm: Edit

Well, number 1 was in the beginning ( in the first 10). the last two are in the last 10

 By Miseryxsignals (Miseryxsignals) on Wednesday, October 08, 2003 - 09:28 pm: Edit

for #1 i think the answer is E) the interior of a circle. my reasoning is that if you draw two dots on a peice of paper, P and Q, and make the line from P to Q a radius, and make a circle using P as the origin, then any point INSIDE the circle will be closer to P than Q, which is on the frontier of the circle.

 By Mekker3 (Mekker3) on Thursday, October 09, 2003 - 01:00 pm: Edit

can someone explain to me what a plane "looks" like... is it infinite?

 By Volleygenius (Volleygenius) on Thursday, October 09, 2003 - 01:08 pm: Edit

for number one u have to draw a perpendicular bisector of the two lines. This line divides the segment created when u join the two lines and everything on the side with P will b closer to P