Two math questions from the collegeboard red book :/

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1

<p>I dont know why I can't figure both of these problems out, maybe im just overlooking them. </p>

<p>22) A ball is dropped from 192 inches above level ground and after the third bounce it rises to a height of 24 inches. If the height to which the ball rises after each bounce is always the same fraction of the height reached on it's previous bounce, what is this fraction?</p>

<p>23) 1/X= 0.0N
1/Y= 0.00P</p>

<p>The fractions 1/X and 1/Y can be written as decimals as shown above, where N and P represent different digits. Which of the following is equal to 1/X(Y) if S=N(P) and S is a digit?</p>

<p>A. 0.0000S is the answer</p>

2

<p>I get the first question now, sorry.</p>

3

<p>is the first one 1/2? 192 96 48 24?</p>

4

<p>Yea (1/2) is the answer</p>

5

<p>Assuming that you meant 1/X * 1/Y, this is the way I do it:</p>

<p>Write it down like a long-multiplication problem:</p>

<p>



 0.00P</p>

<h2>x 0.0N</h2>

<pre><code> S  <- you know that N(P) is S and it's a digit
</code></pre>

<p>

</p>

<p>Then you have S.0, so move the decimal to the left the correct number of places (2 + 3 = 5 places, from .0N and .00P respectively). Result is 0.0000S</p>

<p>EDIT: Forgot to mention that if it's easier for you, replace P and N with numbers that when multiplied result in a single digit. i.e. 2=P, 3=N, 2*3=6=S.</p>

6

<p>So basically the most important thing to know is that because S is a digit and there are 5 0's, I would simply move S 5 places to the right from S.0 to 0.000S.</p>

7

<p>^That's correct.</p>

<p>Another way to look at question 374 / 23:
1/x = N/100
1/y = P/1000
1/(xy) = (NP)/100000
1/(xy) = S/100000
1/(xy) = .0000S</p>

<h2>Answer (A).</h2>

<p>Even faster (see Hippo's Edit):
assume N = 1, P = 1
then S = NP = 1
1/x = .01
1/y = .001
1/(xy) = (.01)(.001) = .00001 = .0000S.</p>