Math SAT HELP

Test Preparation SAT Preparation
1

<p>Please help and explain if you can, I really dont understand them</p>

<ol>
<li><p>If an integer is added to its square the units digit of this sum could be?
A. 1 B. 2 C. 3 D. 4 E. 5</p></li>
<li><p>Each "word in a special code is a three digit number. If no word in the code can begin with a 1 or 0, what is the greatest number of different words the code can contain?
A. 28 B. 512 C. 800 D. 900 E. 1000</p></li>
</ol>

<p>3.If n and p are integers greater than 1 and if p is a factor of both n+3 and n+10, what is the value of p?
A. 3 B. 7 C. 10 D. 13 E. 30</p>

<ol>
<li><p>A set of numbers is called a "unified" set if for every number x in the set, there is a number y in the set such that xy=1. If the set {0.1, 0.2, 0.5, 5, 10, k} is a unified set, what is the value of k?</p></li>
<li><p>Two cylinderical candles of the same height and diameter burn at the same uniform rate. Each takes 4 hours to be consumed. If the first candle is lit at 8:00pm and the second at 9:00 pm, at what time will the second candle be exactly 3 times as tall as the first?</p></li>
</ol>

<p>A. 9:30 pm B. 10:00 pm C. 10:30 pm D 11:00 pm E. 11:30 pm</p>

<ol>
<li>15 cubic centimeters of water was poured into each of the empty rectangular containers above. THe containers rest on a level surface. What is the difference in the height of the water between container M and container L in centimers?</li>
</ol>

<p>In the diagram Container L is a 3x3x3 cube with no top lid and Container M is a 3x2x3 cube with no top lid.</p>

2

<ol>
<li>B</li>
</ol>

<p>Just did really simple guess and check. If you use the integer 3, then you get 3 + (3^2) = 12… with a units digit of 2. B is your answer.</p>

<p>Don’t have time to do rest right now, but may come back to it later! Good luck</p>

3

<p>Okay thank you</p>

4

<ol>
<li>B</li>
</ol>

<p>Just plug in numbers really quickly and see which you could get.</p>

<p>2) C . THis is like the counting principal.</p>

<p>8 options x 10 options x 10 options = 800 options</p>

<p>(We can use 2,3,4,5,6,7,8,9 for the first digit) and (1,2,3,4,5,6,7,8,9,0 for the next two)</p>

<p>3) the answer i think is 7 (B).</p>

<p>Because since p is a factor of n+3 and n+10, you can see the difference between the two numbers is 7. If its a factor of both, then it must be 7.</p>

<p>quick test, let n =11.</p>

<p>11+3 =14 </p>

<p>11+10=21</p>

<p>both have seven as factors.</p>

<p>4) the answer is K=2 i believe. Since in the set all the numbers there have a corresponding number to make them equal to 1 when multiplied together, except 0,5. SO, 0.5k = 1, k=2.</p>

<p>5) weird ~ </p>

<p>6) The second container will be full, (so 3cm high)
and the first container will be 3 x 3 x h =15
9h = 15
h = 15/9 cm tall. </p>

<p>3 - (15/9) = 27/9 - 15 / 9 = 12/9 or 4/3. So the difference between the containers is 4/3cm or 1.33cm.</p>

<p>(i think)</p>

5

<p>Thank you sooooo much!</p>

6

<ol>
<li><p>E I just used guess and check and plugged in numbers. Let say their 4cm each. At 9, cylinder 1 is 3cm and and Cylinder 2 in 4 cm. At 11, cylinder 1 is 1cm and cylinder 2 is 2cm. At 11:30, Cylinder 1 is 1/2 and Cylinder 2 is 3/2.</p></li>
<li><p>For this I got 0.83333, but I think I’m wrong</p></li>
</ol>

7

<ol>
<li><p>B
11+11^2=132, 2 is the ones (units) digit. </p></li>
<li><p>C</p></li>
</ol>

<p>On the first number of the code, you have 8 possible digits as 0 and 1 are omitted. You can still use 1,2,3,…9
On the second number, you have 10 possible digits (1,2,3,…9). Same for the third number. Multiply all the possible digits from each category, 8x10x10, and you get 800. </p>

<ol>
<li><p>B
(4)+3=7, and (4)+10=14
Both 7 and 14 are divisible by 7. </p></li>
<li><p>K=2
0.1(10)=1, 0.2(5)=1, and now the only unpaired number remaining is 0.5
So you could solve for k by using the following equation: 0.5(k)=1. k=2 </p></li>
<li><p>C</p></li>
</ol>

<p>Lets say both candles are 3 cm tall and burn at an incremental rate of 1 inch per hour.</p>

<p>Here is a table for both candles throughout time:</p>

<p>Candle 1 | Candle 2
Time/Height | Times/Height</p>

<p>8:00 PM/3 in | 8:00 PM/3 in (Still not lit)
8:30 PM/2.5 in | 8:30 PM/3 in (Still not lit)
9:00 PM/2 in | 9:00 PM/3 in
9:30 PM/1.5 in | 9:30 PM/2.5 in
10:00 PM/1 in | 10:00 PM/2 in
10:30 PM/0.5 in | 10:30 PM/1.5 in <em>DING DING DING</em>
11:00 PM/ 0 in | 11:00 PM/1 in</p>

<ol>
<li>The total volume of Container L is 27 cubic cm. The total volume of container M is 18 cubic cm. If you fill both containers with 15 cubic cm, then you would get a height of 15/27 for Container L and a height of 15/18 for Container M. 405/486 (M) - 270/486 (L) is equal to 5/18 cubic cm (Probably right, but not sure). </li>
</ol>

<p>I’m sorry if any of that was a bit confusing! Just tell me and I’ll try to re-explain it to you!</p>

8

<p>Achilles, the problem with your answer for n°5 is that the candles burn out in 4 hours not 3 hours… so it’s 11:30 not 10:30, I used the same work as you.</p>

9

<p>The answer I gave for #6 is wrong, oops!</p>

10

<p>@Trielite: Yes my bad, I was in a rush when answering these questions and completely missed the part about the 4 hours. I redid the problem, and yes you are correct, the answer would be E;11:30.</p>