<ol>
<li><p>if n/(n-1) x (1/n) x n/(n+1)=5/k for positive integers n and k, what is the value of k?
a. 1 b. 5 c. 24 d. 25 e. 26
answer is c.</p></li>
<li><p>ahmad has containers of two different sizes. the total capacity of 16 containers of one size is x gallons, and the total capacity of 8 containers of the other size is also x gallons, and x>0. in terms of x, what is the capacitiy, in gallons, of each of the larger containers?
a.4x b. 2x c. x/2 d. x/8 e. x/16
answer is d.</p></li>
</ol>
<p>Basically, for the first one, you can easily get it to the following format (n/(n^2-a))=5/k This can be transformed to the following equation, 5n^2-kn-5=0. From here on I cheated because I didnt feel like factoring manually. I plugged it into TI 89 and used the factor( ) function while plugging in answers in place of k. The only answer (k=24) that allowed n to be an integer was C. It factored into (n-5)(5n+1). Thus it is the only possible combination of positive integers k and n. You could also do the manual factoring, but its time consuming and boring.</p>
<p>Not sure whats hard about the second problem. It provides a bunch of unneeded info. If you need fewer containers to store the same volume x, then it means that the containers with quantity = 8 are larger. If x is the total volume stored in 8 containers, the volume per one container is x/8. Answer D.</p>
<p>1) Multiply everything out and you get n/(n^2 - 1) = 5/k</p>
<p>Now, you just want to plug in values for k and see if you can get a corresponding positive integral value of n.</p>
<p>k = 1
n/(n^2 - 1) = 5
n = 1 makes the equation undefined, and after plugging in n = 2, 3, etc. you’ll find that the left side of the equation gets smaller and smaller and will never be larger or equal to 1.</p>
<p>k = 5
n/(n^2 - 1) = 1
n = 1 makes it undefined. For the same reason as above, n = 2, 3 will just make the expression smaller and never equal 1.</p>
<p>k = 24
n/(n^2 - 1) = 5/24
n = 2 gives 2/3, n = 3 gives 3/8 (we see that we’re getting closer to 5/24 so keep going), n = 4 gives 4/15, n = 5 gives 5/24. We have a winner.</p>
<p>2) Let the total capacity of both sized containers (the variable x) be 16 gallons. The capacity of the smaller containers is 16 gallons/16 containers = 1 gallon/container.</p>
<p>The capacity of the larger containers is 16 gallons/8 containers = 2 gallons/container. </p>
<p>Now replace x with 16 in the answer choices and see which gives you 2.</p>
<p>A 64
B 32
C 8
D 2
E 1</p>
<p>Answer is D, x/8.</p>
<p>Alternatively, if you can think your way through the variables, realize that the smaller # of containers will be larger in size because a fewer number of containers has the same total capacity as the greater number of containers. If x is the total capacity and there are 8 containers, then the capacity per large container is (x gallons)/(8 containers) = x/8 gallons/container</p>
<p>thanks a lot :)</p>
<p>I still don’t get that first question =(</p>