# More Math Questions...

<p>I got these from Killer Math from Princeton Review</p>

<li><p>39 points are placed inside or on the surface of a perfect sphere. If 60% of fewer touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere?
a. 7
b. 11
c.13
d. 23
e. 38
<li><p>If Q, R, S, T, U, V are six unique points along a circle such that six chords QU, RS, ST, TU, UV, and VQ are equal in length, which of the following is the circles diameter?
a. QS
b. UT
C. SV
D. (QR+QS)/2
E. (UV+RS+TQ)/3
<li><p>How many three-digit integers exist where the sum of all the digits is 7, and even and odd digits alternate?
a. 1
b. 2
c. 4
d. 6
e. 8
Is there a quick way of solving this besides listing all the numbers out?</p></li>
<li><p>On a number line Q=1 and R = -2. How many points on the number line are twice as far from R as they are from Q?
a. 0
b. 1
c. 2
d. 3
e. Cant be determined
<li><p>At Julie’s Jewelry Inc, there are necklaces, bracelets, and rings for sale. If \$30.00 were to be added to the price of a necklace, the cost would be the same as that of the sum of 90% of the price of a bracelet and 75% of the price of a ring. If \$20 were to be added to the price of a bracelet, the price would be the same as that of the sum of 3/5 of the price of a necklace and 3/4 of the price of a ring. If the price of a ring is the same as that of the sum of 40% of the price of a necklace and 10% of the price of a bracelet, then how much do two rings cost?
a. \$25
b. \$50
c. \$100
d. \$150
e. \$200
Is there a faster way of solving thing then just doing a system of equations?</p></li>
<li><p>Two parallel lines have equations ay+bx=4a and y-8 = 2x. Which of the following is the equations of a third line that is equidistant from these lines?
a. y = 2x - 3b/a
b. y = -ax/b+6
c. y = -bx/a - 6b/a
d. y = -bx/2a + -6b/a
e. y = 2x - 6b/a
</ol>

<p>Any help would be appreciated. Thanks :D</p>

<p>ok for the first one i think this is how you do it</p>

<p>theres 39 points, at in the best situation 23.4 (60% of 39) touch the surface</p>

<p>then two points make a line, so out of 23 points you can get 11 lines, note that this assumes that all the points cooperate to form diameters</p>

<hr>

<p>45) draw R and Q on a number line, their difference is 3, so when the point is 2 away from R it is 1 away from Q.
The second way is when the point is 4, in which case it is 6 away from R and 3 away from Q</p>

<hr>

<p>54)</p>

<p>put boht equations into slope-int form</p>

<p>you get :
y=2x+8
y=(-b/a)x+4</p>

<p>since the lines are parallel you know -b/a = 2
so now just find the line inbetween these two lines, which would be y=2x+6</p>

<p>but they throw in a trick, convert the answers so that the -b/a is two</p>

<p>choice a, y=2x -3b/a = 2x + 3*2 = 2x+6= your answer</p>

<p>28.)</p>

<p>2 _ _
2 1 4
2 3 2
2 5 0</p>

<p>4 _ _
4 1 2
4 3 0</p>

<p>6 _ _
6 1 0</p>

<p>Answer: 6. I thought listing them out was very fast, at least much faster than trying to figure out a fast way to do it!</p>

<ol>
<li>It looks like there are two main options: you could try to work backwards and plug in each of the choices until you get the right answer, or you could use the system of equations. The first option doesn't work. You'd still have to do a system of equations. So system of equations is the right way to go.</li>
</ol>

<p>Are you sure those are the right chords for #24? I don't think it's possible to have three equivalent yet distinct chords from one point (QU, TU, UV).</p>

<h1>28 what neo said, the chords don't seem to match up. Only way to make six chords equal is to align them hexagonally i think...</h1>

<h1>50. systems is the way to go</h1>

<ol>
<li>it's a system but solved quickly.
n+30 = .9b+.75r
b+20 = .6n+.75r
r = .4n+.1b</li>
</ol>