BB2 Math questions?

Test Preparation SAT Preparation
1

<p>These problems are time-consuming for me because I end up plugging in answers. Can someone show me how to do these problems?</p>

<p>1) P.418/ #16</p>

<p>A four-digit integer, WXYZ, in which W, X, Y, and Z each represent a different digit, is formed according to the following rules.
1. X = W + Y + Z
2. W = Y + 1
3. Z = W - 5
What is the four-digit integer?
Answer: 5940</p>

<p>2) P.485/ #13</p>

<p>If n is a positive integer and 2^n + 2^(n+1) = k, what is 2^(n+2) in terms of k?
Answer: 4k/3</p>

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<ol>
<li>factor. k = 2^n(1 + 2) = 3 * 2^n. so 2^n = k/3, and multiplying both sides by 2^2, we get 2^n+2 = 4k/3</li>
</ol>

3

<ol>
<li>WXYZ, in which W, X, Y, and Z each represent a different digit, is formed according to the following rules.</li>
<li>X = W + Y + Z</li>
<li>W = Y + 1</li>
<li>Z = W - 5
Since X is obviously the largest of the numbers let it equal 9.
Next, we see that W is the second largest - and since X, Y, W, and Z are all different numbers we know from the second equation that W can’t be greater than 5, because 2W -1 + Z = 9 and if we let Z = 0 then we have: 2W = 10 or W = 5.</li>
</ol>

<p>Thus we have meet all of our conditions and Y = 4 and Z = 0 giving us the desired number: 5940</p>

4

<p>Thanks for the replies. Spratleyj, could you explain a little more? How did you know X=9? Is there a systematic way to do that problem? What I did was I first substituted and turned the first equation to X = 3Y - 3. I knew Y could not be 5 or greater or else X would be a two digit number. Then I just kinda plugged in numbers from there…</p>

5

<p>Anyways here’s two more I need help with :P</p>

<p>3) Pg. 518/ #14
t^2 - K^2 < 6
t + k > 4
If t and k are positive integers in the inequalities above and t > k, what is the value of t?</p>

<p>I first factored out t^2 - k^2and because t + k is 5 or greater, I knew t - k = 0 or 1. From there I did not know what to do so I just put in numbers. </p>

<p>4) Pg. 527/ #6
If x != 0 and x is inversley proportional to y, which of the following is directly proportional to 1/x^2?</p>

6

<p>When doing those type of problems just make sure you understand what the conditions are: there is only going to be one correct answer - you know X is the greatest and there is no condition such that X can’t equal 9, therefore x = 9. </p>

<p>x! = 0 , and x is inversely proportional to y, which of the following is directly proportional to (1/x^2)</p>

<p>Am I reading this correctly?</p>

7

<p>stupid lag = double post…</p>

8

<p>Okay, I understand the WXYZ problem now. </p>

<p>I meant
“If x is not equal to 0, and x is inversely proportional to y, which of the following is directly proportional to 1/(x^2)?”</p>

9

<p>x = 1/y</p>

<p>x^2 = 1/y^2
y^2 = 1/x^2</p>

<p>Which reads as “y^2 is directly proportional to 1/x^2.”</p>

10

<p>

</p>

<p>Another method is to start with conditions 2 and 3. This eliminate the step of “guessing” what X is when starting. </p>

<p>From 3 we lean that Z = W - 5 => W has to be at least 5</p>

<p>From 2 we learn that W = Y + 1 => Y has to be at least 4</p>

<p>** The problem is really solved at this stage, but let’s continue for verification.</p>

<p>Since X = W + Y + Z, X cannot exceed 9, we know that z has to be zero (because W plus Y cannot be lower than 9). It also means that X = 9 and that W has to be 5, and Y has to be 4.</p>

<p>Replacing the numbers shows that WXYZ is 5 9 4 0</p>

<p>PS Remember that the ojective of ETS is to make you lose time and that the test writers LOVE to add a little curve. In this case, they WANT you to start plug in numbers because they know most people won’t use a ZERO as a plug. Accordingly, RESIST the urge to plug numbers in without trying to SOLVE the problem by checking the conditions and using simple reasoning.</p>