<p>Section 2: #16, 17, 18
Section 6: #14 (It says there are 25 trays, but it also says there are 15 of trays and 21 of trays. Ummm... it first says there are 25 trays first than how are there 36 trays all together?).
Section 6: #18
Section 8: #10 (Couldn't all the answer choices be correct?)
Section 8: #16</p>

<p>THANK YOU LADIES AND GENTLMEN! THANK YOU FOR YOUR CONTRIBUTIONS!</p>

<p>16 - This is basic counting. 1 block + 1 block + 1 block + 1/2 block = 3.5 blocks.</p>

<p>17 - Really hard to explain online...just draw out different possibilities when the firetruck goes left then down then left, down then left then down, etc. Don't rule out a larger answer choice until you're absolutely sure you've exhausted every possibility.</p>

<p>18 - again, hard to explain. Draw out the basic points (3 blocks N W S and east). Then draw out the less obvious points (2 blocks N 1 block east, etc.). You find yourself drawing a square (diamond).</p>

<p>Section 6</p>

<p>14 - Use this formula: Total = Group 1 + Group 2 - Both
25 = 15 + 21 - Both
Both = 11</p>

<p>18 - I did this algebraically since there are no answer choices to work with</p>

<p>Let PQ = RS = y and PS = x.</p>

<p>PT is 2/5 of PS, so TS is 3/5 of PS aka 3/5 x.</p>

<p>We were looking for the area of the rectangle (xy) and we got it.</p>

<p>I didn't look at the answers but I assume these are right. I don't have time right now to do the rest of the problems but I'll tackle them if no one else has later.</p>

<ol>
<li><p>Look at it like streets in a grid. Just count how many blocks you have to travel to W, but you have to stay on the line. 3 1/2 is the answer. </p></li>
<li><p>Picture it as a square. You can obviously go on the sides of the square, so 2. How about go W 1, S1, W1, S1. Similarly, S1, W1, S1, W1 also takes you there. For the other 2 ways, it's S1, W2, S1, and W1, S2, W1.</p></li>
<li><p>Just draw every point 3 unit lenghts, and it's easy to see it's a square.</p></li>
</ol>

<p>S. 6</p>

<ol>
<li><p>25 in total. 21 have a plate, so 4 don't have a plate, and are thus cup only. 15 have a cup, so 10 don't, so 10 are plate only. 25 - 10 - 4 = 11 cup & plate</p></li>
<li><p>1/2 * RS * ST = 7.
RS * PS = Area</p></li>
</ol>

<p>PT = 2/5 PS, so ST = 3/5 PS</p>

<p>1/2 * 3/5 * PS * RS = 7
PS * RS = 70/3</p>

<p>S. 8</p>

<ol>
<li><p>They all took half the rope, so the answer has to be a multiple of 1/2. i.e. S1 had 1/2 the rope, S2 had 1/4, S3 had 1/8, S4 had 1/16.</p></li>
<li><p>Easy trick. You want a value of x such that t is an integer. Since + 1/x is in the equation, it's clear that the only values which will work are -1 or 1. Check -1 and you'll see it works out and t = -2.</p></li>
</ol>

<p>Edit: I was sidetracked for like an hour so posted too late :{</p>

<p>Section 8 No.10
The answer is C or "1/16"
because
the denominator has to be a power of 2. Imagine you have a rope and divide into two equal pieces. You'll have 1/2 of the rope. Then the next person will divide his 1/2 of the original rope into two equal parts creating 1/4 of the original rope. The process will go on, each consecutive person creating 1/8 and 1/16, 1/32... fractions of the original rope. </p>

<p>Section 8 No.16
The answer is D or "-2"
If x+(x/1) equals an integer and x is an integer, the only two possible integers that can make x+(1/x) an integer are -1 and 1. So, if you substitute 1 in the equation you'll get 2 but that isn't among the answer choices; you try -1 which yields -2, which is D.</p>

<p>10 - If each time the rope is divided into two halves, then the possible rope sizes are 1/2, 1/4, 1/8, 1/16, 1/32 and so on (each time being multiplied by 1/2). Hence 1/16 is the answer.</p>

<p>16 - Notice that all the possibilities for t are integers, meaning that the only two possibilities for x are -1 and 1 (since anything but -1 or 1 would make 1/x a fraction and hence x + 1/x, or t, wouldn't be an integer)</p>

<p>t = 1 + 1/1 = 2
t = -1 + 1/-1 = -2</p>

<p>2 isn't an answer choice so -2 is the answer.</p>