Please help me on these math questions that I failed miserably on

Test Preparation SAT Preparation
1

<p>Bolded choice = Correct Answer
[X] = My Incorrect Answer
[O] = Omitted</p>

<hr>

<ol>
<li>The square of x is equal to 4 times the square of y. If x is 1 more than twice y, what is the value of x?</li>
</ol>

<p>A. -4
B. -1/2
C. -1/4 [X]
D. 1/4
E. 1/2</p>

<hr>

<ol>
<li>Meredith has a red hat, a blue hat, and a white hat. She also three sweaters - one red, one blue, and one white - and three pairs of jeans - one red, on blue, and one white. Meredith wants to wear a red, white, and blue outfit consisting of one hat, one sweater, and one pair of jeans. How many different possibilities does she have?</li>
</ol>

<p>A. 3
B. 6
C. 9
D. 12
E. 27 [X]</p>

<hr>

<ol>
<li>f(x) = | 3*x*-17 |
For the function defined above, what is one possible value of a for which f(a)<a?</li>
</ol>

<p>2 [X]
4.25<x<8.5 or 17/4<x<17/2</p>

<hr>

<ol>
<li>A positive integeris said to be "tri-factorable" if it is the product of three consecutive integers. How many positive integers less than 1,000 are tri-factorable?</li>
</ol>

<p>997 [X]
9</p>

<hr>

<ol>
<li>A box contains wood beads, red glass beads, and blue glass beads. The number of glass beads is 4 times the number of wood beads. If one bead is to be chosen at random from the box, the probability that a red glass bead will be chosen is 3 times the probability that a blue glass bead will be chosen. If there are 12 red glass beads in the box, what is the total number of beads in the box?</li>
</ol>

<p>[O] Omitted</p>

<p>A. 20
B. 45
C. 48
D. 60
E. 90</p>

<hr>

<ol>
<li>The figure below shows an arrangement of 10 squares, each with side of length k inches. The perimeter of the figure is p inches. The area of the figure is a square inches. If p = a, what is the value of k?</li>
</ol>

<p>[ ]
[ ][ ]
[ ][ ][ ]
[ ][ ][ ][ ]</p>

<p>[O] Omitted</p>

<p>8/5 or 1.6</p>

<hr>

<ol>
<li>On a square gameboard that is divided into n rows of n dquares each, k of these squares lie along the boundary of the gameboard. Which of the following is a possible value for k?</li>
</ol>

<p>A. 10 [X]
B. 25
C. 34
D. 42
E. 52</p>

2

<p>I’ll try my best to explain the first one.</p>

<p>First I translate the problem and got this:</p>

<p>x^2=4y^2 AND x=2y+1</p>

<p>Now you plus “2y+1” into the the first equation.</p>

<p>Then you get out 4y^2+4y+1.</p>

<p>That equals 4y^2.</p>

<p>So you can subtract that from both sides of the equal sign and you get out this:</p>

<p>4y+1=0. Y has to be -1/4.</p>

<p>Now let us bring back the original equation: x^2=4y^2.</p>

<p>Plugging in -1/4 to the left side, you get 1/16 multiplied by 4, which can be simplified down to 1/4.</p>

<p>Now it’s x^2=1/4.</p>

<p>You probably know the test.</p>

3

<p>Oh wow lol just a simple substitution problem</p>

<p>Dang, I need to stop making careless mistakes</p>

4

<p>I can also explain question five.</p>

<p>I’ll set</p>

<p>wood beads=w
red glass beads=r
blue glass beds=b</p>

<p>Then I translate the information the question gave me to this:</p>

<p>r+b=4w
r=3b
r=12</p>

<p>Now you figure out that 12=3b, so you know that there are four blue beads.</p>

<p>Now just plug that into the original problem so that:</p>

<p>12+4=4w
16=4w
w=4</p>

<p>4+4+12=20</p>

5

<p>Darn it, another careless mistake on such a simple problem. Boo me ><</p>

6

<p>I think I answered the last one before, and the answer just has to have a factor of 4.</p>

7

<p>Question 4: </p>

<p>Just start at 1 X 2 X 3 and maxes out at 990 with 9 X 10 X 11.</p>

8

<p>Question 2
Because Meredith needs an outfit with the colors red, white, and blue, when picking the first item, she can pick any color. That gives us a probability of 1/3. Next, when she picks the second item, she can pick any of the two colors that she did not pick as her first choice. This gives us the probability of 1/2. The final piece of clothing can only be the color she hasn’t picked yet. This gives us a probability of 1/1. When you multiply the probabilities of 1/6 or 1 combination out of 6 possible combinations. Therefore there are 6 possible outfits.</p>

<p>Question 3
For these types of problems, I find it easier to just make educated guesses. For example I would substitute logical choices until I find a number that works. I honestly don’t know the algebraical solution but I found a viable solution within about 10 seconds. Sorry if this doesn’t help.</p>

<p>Question 6
When looking at the figure, by utilizing the geometric properties of squares, you know that the perimeter is equal to 16 times the length of one side of a square, or 16k. 16k=p, so since you know that p=a you can also assume that there are 10 squares for a combined area of 10k^2. By only taking into account the integral components of the previous equations, you can extrapolate another equation, 10k=16. When you solve for k, you come out to 8/5 or 1.6.</p>

<p>I hope I explained everything ok.</p>

9

<p>for question 7, think about all the the squares on the outside. The total amount of all those squares on the outside(k) should be 4 * (n - 1), so that’s k = 4n - 4, the thing you have to realize is that n has to be an integer, so out of all the possible answers you are given, only choice E 52 satisfies this equation with n being an integer. 52 = 4 * 14 - 4</p>