SAT Hard Math Questions May 11 Help

<p>Hey guys!</p>

<p><a href="http://puu.sh/3BoXG.jpg%5B/url%5D"&gt;http://puu.sh/3BoXG.jpg&lt;/a&gt;&lt;/p>

<p>This one is weird, the answer is 1000 but I have no idea why!</p>

<p><a href="http://puu.sh/3Bp1U.jpg%5B/url%5D"&gt;http://puu.sh/3Bp1U.jpg&lt;/a&gt;&lt;/p>

<p>I did come to the answer "8521" but it took me a while. Is there another way to figure this out or a better method?</p>

<p>And finally!</p>

<p><a href="http://puu.sh/3Bp3J.jpg%5B/url%5D"&gt;http://puu.sh/3Bp3J.jpg&lt;/a&gt;&lt;/p>

<p>I got the answer but I had to write all the possibilities out. Is there an equation? </p>

<p>Thanks!</p>

<p>1) Volume of a solid = height * length * width = 20 * 5 * 10 = 1000 cm³
1 cubic meter = 100 * 100 * 100 = 1,000,000 cm³</p>

<p>Hence, we need 1000 of these solids to fill 1 cubic meter, since 1000 * 1000 cm³ = 1,000,000 cm³</p>

<p>2) I think the fastest method is by trial and error. It doesn’t work for 9621, but it does for 8521. Took me about 30 seconds to solve. </p>

<p>3) Basic combinatorics. He can take 3 different breads (but not the same!), so imagine it like 3 bags - A B C. In the first bag, A, he can put 4 different breads. In the second, since he cannot take the same as in A, 3. And the third, 2 different breads.</p>

<p>4 * 3 * 2 = 24</p>

<p>Killparis, the actual answer for 3 is 4 buddy. </p>

<p>And thank you for 1 and 2. How did you get 1,000,000? Is it because 1 X 1 X 1= 1 cubic meter and that would result in 100 X 100 X 100= 1,000,000?</p>

<p>Oh. That’s true. I’ve read the question wrongly, my apologies. (it’s midnight here :slight_smile:
In that case: let’s call these breads A B C D. The customer can take either</p>

<p>A B C
A B D
B C D
C A B</p>

<p>We don’t go any further since A B C is the same as C B A, order does not matter in this case. </p>

<p>And yes. For example a cube, with a side of length 10 centimeters have volume of 10 * 10 * 10 = 1000 cm³. </p>

<p>The catch here is that they say “1 cubic meter”, which is 1 m³. We know that 1 m = 100 cm, so we have that 1(100cm)³, which is equal to 1,000,000 cm³.</p>