<ol>
<li>Kevin is 3 years younger than Nora. If N represents Nora's age now, what was Kevins age 4 years ago in terms of N?</li>
</ol>
<p>What is the trick to answering problems like these^^?</p>
<ol>
<li>If the area of each face of a cube is 49 square inches, what is the total length in inches of all the edges of the cube?</li>
</ol>
<p>is the trick just to know that a cube has 12 edges?</p>
<ol>
<li><p>If (x+y)^2 -(x-y)^2 = 84 and x and y are positive integers, which of the following could be a value of x+y?</p></li>
<li><p>A gas tank with a capacity of 18 gallons is empty. A pump can deliver g gallons of gas every t seconds. In terms of g and t, how many seconds will it take this pump to fill the tank?
A)18t/g
B)18g/t
C)18gt
D)g/18t
E)gt/18</p></li>
</ol>
<p>I did this by plugging in numbers. What's the best/most efficient/most accurate way to do these sorts of problems? and whats the algebraic way?</p>
<p>5.
k = kevin’s (current) age, n = nora’s (current) age
We’re solving for k-4
k = n-3
k-4 = n-3-4
k-4 = n-7
Answer is n-7.</p>
<p>The tricks to a problem like this are defining your variables and not getting confused by the wording. They’re trying to trick you with the different years, but once you translate it into algebra, it’s a very simple math problem. The hard part is setting it up.</p>
<ol>
<li>Area of one face of a cube = s^2
s^2 = 49 in.
sqrt(s^2) = sqrt(49)
s = 7
The answer is 7 in.</li>
</ol>
<p>The trick to this question is to be familiar with the properties of a cube. The question itself is actually pretty straightforward. If you know that all edges of a cube are equivalent (and that therefore each face is a square), then you can figure out that the area is just the edge lengths squared. You should also know (though it’s not important for this question) that the volume of a cube is s^3 (or “the length of an edge cubed”).</p>
<ol>
<li><p>Can’t tell you the best way to answer this because the answers aren’t listed. You might note, though, that there’s a difference of squares there that would probably be helpful to exploit.</p></li>
<li><p>Rate * Time = Distance (or, in this case Rate * Time = Gallons Filled)
So, (G/T) * Total Number of Seconds = 18
We’re solving for Total Number of Seconds, so just divide by G/T:
Total Number of Seconds = 18/(G/T)
18/(G/T) = 18T/G
The answer is A.</p></li>
</ol>
<p>The only trick there is to recognize the problem type, and then to realize that the rate that the pump is filling the tank at is the number of gallons per the number of seconds (or, the number of gallons divided by the number of seconds). Think about other “rates” that you know, like “miles per hour” or “rotations per minute.”</p>
<p>Although, 84 is a pretty good indicator of how high you’ll have to go, so you know you only have to go to 10^2 and figure out from there what gives you 84 by finding the combinations that add up to 10.</p>