<p>I was doing these problems in a practice test but had some difficulties. It would be great if you could tell me how to do it. Thanks!</p>
<p>1) The digits 3,6,7 and 8 will be used without repetition to form different 3-digit numbers. Of all such numbers how many are greater than 500</p>
<p>2) y^5 = 50 and z^2 = 10 , what is the value of y^10z^-2</p>
<ol>
<li><p>The first digit must be 6,7, or 8. So three choices for the first digit, three for the second, two for the third. 3<em>3</em>2 = 18</p></li>
<li><p>From the first equation, y^10 = 50^2 = 2500. If we take the second equation and raise both sides to -1 power, we get z^(-2) = 1/10. Multiplying, (y^10)(z^(-2)) = 250.</p></li>
</ol>
<p>Alright so I understood number 2 completely, but number 1 still confuses me. So you said the first digit has to be 6,7, or 8 which makes sense. Why does it have to be 3 for the second one and 2 for the third?</p>
<p>Thanks :)</p>
<p>It has to be 3 for the second one because after you choose a number for the first slot from 6, 7, or 8 there are only 3 numbers left that you can choose from for the second slot: 3 and the two remaining numbers. This in turn only leaves you with 2 numbers to choose from for the third. </p>
<p>Therefore, the answer is 3 x 3 x 2 = 18.</p>
<p>Thanks :). I think I just have one more math question:</p>
<p>If a square has a side of length x + 4 and a diagonal of length x+8, what is the value of x?</p>
<p>The diagonal is sqrt(2) times the side length (think 45-45-90 triangles)</p>
<p>x+8 = (sqrt(2))(x+4)</p>
<p>x+8 = x sqrt(2) + 4 sqrt(2)</p>
<p>8 - 4 sqrt(2) = x sqrt(2) - x = x (sqrt(2) - 1)</p>
<p>x = (8 - 4sqrt(2))/(sqrt(2) - 1)</p>
<p>By rationalizing the denominator, you should get x = 4sqrt(2).</p>
<p>Are these problems from the blue book because they seem kinda tough for blue book standards… ?</p>
<p>@cinnamin</p>
<p>I don’t remember if these are from the blue book, but they are all reasonable for SAT questions - they are Level 4 and 5 questions.</p>
<p>^ yeah they are i guess. they are all familiar…
can some someone help ME out with this one?
[The</a> Official SAT Question of the Day](<a href=“The SAT – SAT Suite | College Board”>The SAT – SAT Suite | College Board)</p>
<p>It says… that In the xy-plane, the graph of the equation y=-2(x^2)+bx+c assumes its maximum value at x=2 . What is the value of b?</p>
<p>Dunno… the answer has the (x-a)^2-k formula which I am not familiar with so… can someone explain?</p>
<p>The maximum value occurs at x=-b/(2a) = -b/(-4) = b/4. So b/4 = 2, and b = 8.</p>
<p>^ thank u so much! Do u have any other problems for practice… test is tomorrow u know…
anyone else has too?</p>
<p>^ thank u so much! Do u have any other problems for practice… test is tomorrow u know…
anyone else has too?</p>