Weird math problem help!

Test Preparation SAT Preparation
1

<p>Hello! Whilst doing a practice test came upon a difficult problem and can't solve it.
In ∆MPQ above (<a href="http://oi52.tinypic.com/2ilo94z.jpg%5B/url%5D"&gt;http://oi52.tinypic.com/2ilo94z.jpg&lt;/a&gt;), the measure of angle M is 30 and the measure of angle Q is 45. What is the length of segment MQ?
(A)15
(B)20
(C)5√2
(D)5√3
(E)(5√3)+5</p>

<p>I really need to understand how to solve this problem, it might come up in the October test!</p>

2

<p>The answer is E without doing much calculations. It is a typical SAT question.</p>

3

<p>Drop a perpendicular line from angle P creating a right angle in each of the now two triangles. Call that point of intersection R. Triangle MPR is 30-60-90. Since the side opposite Angle R is 10 we know that MR = 5. Line PR is (5 sqrt 3). Triangle QRP is a 45-45-90 triangle. Since side PR = (5 sqrt 3), we know that QR is also (5 sqrt 3). Add MR and QR together. 5+ (5 sqrt3). Answer E.</p>

4

<p>nevermindd</p>

5

<p>Correction. The answer is the same but side PR = 5 and MR = (5sqrt3) since line PR = 5, QR = 5. Choice E (5 SQRt3) + 5</p>

6

<p>Thanks all who answered!!! Especially Yankee Belle, thank you.</p>

7

<p>Hey can you help me with a couple of more problems? (two more problems that came up today) If yes the problem is here: <a href=“http://oi53.■■■■■■■.com/2ahu0dl.jpg[/url]”>http://oi53.■■■■■■■.com/2ahu0dl.jpg&lt;/a&gt;, <a href=“http://oi52.■■■■■■■.com/nqtthk.jpg[/url]”>http://oi52.■■■■■■■.com/nqtthk.jpg&lt;/a&gt;. Thank you.</p>

8

<p>For the first one: Find the area of the large triangle AC = 9 BC = 4 so area of ABC =36/2=18. Then subtract the area of BDC which is 4*3/2 =6. 18-6 = 12.</p>

<p>The Number line took a little longer. I’m going to go through my process first. Because x+y/2 is larger than both x and x+y you know that x + y is negative. I gave values to the tick marks. I made C = 0, x=-3, y=4 because x+y = -1.That didn’t work because there is no letter at 4. Next I made D = 0, x= -6, x +y = -4, and x+y = -2. That worked. y=2 or E. So trial and error worked.
Then I looked to find an algebraic way. Using absolute values would be faster .<br>
!x +y! = x+ 2. !x+y!/2 = x +4 so y has to be x +8. Count 8 spaces from x and you get to E. I hope that makes sense.</p>

9

<p>Does anyone have a simpler/more lucid explanation for the last question? (Number line)</p>

10

<p>I got the answers of each and every question in less than 30 seconds. I have to admit that the last question took me the longest, probably 20 to 25 seconds, to get the answer. I know how to do it, but it is difficult to explain it especially in writing without being able to point to the figure.</p>

11

<p>easiermath - give it shot at explaining the number line. I know mine is definitely not clear.</p>

12

<p>I prefer the method with made up numbers. But if you prefer algebra:</p>

<p>Let a = the difference between any 2 marks on the line.</p>

<p>Since x+y is 2 clicks to the right of x, you know y = 2a</p>

<p>Then, since (x+y)/2 is 2 clicks to the right of (x+y), you get:</p>

<p>(x+y)/2 = x+y +2a and then substitute y = 2a to get</p>

<p>(x+2a)/2 = x+ 4a</p>

<p>x+2a = 2x + 8a</p>

<p>x= -6a</p>

<p>So now you know that y (which = 2a) is 8a greater than x, or 8 clicks on the line, which takes you to point E.</p>

<p>But again, messing around until you find numbers that fit is probably better.</p>

13

<p>^ cool method. :)</p>