Are you smart enough to solve this math problem?

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1

<p>Hi, the following two math questions are from kaplan premiere program 2008 edition pg 288 practice questions. Please solve and explain why the answer is so... please..</p>

<p>Q2. *i cant post pictures, sorry:: the figure is:
-a circle within a circle. The small inner circle is white, and everything else outside that little circle is shaded. *like a wheel of a car.</p>

<p>In the figure above, what is the maximum number of nonoverlapping regions into which the shaded area can be divded using exactly two straight lines?</p>

<p>A) 3 B) 4 C) 5 D) 6 E) 7</p>

<p>The answer is C) 5, but i have no idea why. I don't even understand the question</p>

<p>Q4. If p-q=4 and r is the number of integers less than p and greater than q, then which of the following could be true?
I) r=3 II) r=4 III) r=5</p>

<p>A) I only B) II only C) III only D) I and II E) I, II, and III</p>

<p>answer: D) i and ii , again, I don't get why.</p>

2

<p>Q2 means if you slice the shaded area using 2 slices, how many sections can you get? I can visualize how you can get 5, but it's kind of hard to explain.</p>

<p>For Q4 I imagined a number line, with p 4 more to the right of q. Then r is the number of integers between q and p. If p is 6 and q=2, then r=3, because r is made up of 3,4,and 5. Then I imagined if q is 1/2 and p is 4 1/2, then r=4, because 1,2,3,and 4 are in between 1/2 and 4 1/2. And using the number line figure in your head you should be able to visualize why there can't be 5 integers in between two numbers that are only 4 away from each other.</p>

3

<ol>
<li> p-r-1 = q --> p-q = r+1 = 4 --> r=3</li>
</ol>

<p>since p and q aren't necessarily integers, r can also be 4.</p>

4

<p>I think I found the solution for number Q2. Imagine the donut shaped figure.
here
<a href="http://i325.photobucket.com/albums/k372/suatkilic/wierdquestion.jpg%5B/url%5D"&gt;http://i325.photobucket.com/albums/k372/suatkilic/wierdquestion.jpg&lt;/a>
Q4 is already answered by thiscouldbeheavn</p>

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<p>Haha, the quintessential donut question <3</p>

6

<p>Q4. Just the numbers:</p>

<p>Arbitrarily assume p=4, q=0,
there are 3 integers between them (1, 2, 3), so
r=3.</p>

<p>Let's now make p and q non-integers.
p=4.5, q=.5,
there are 4 integers between them (1, 2, 3, 4), so
r=4.
Answer D.</p>

7

<p>Thank you so much for the explanations!!!</p>

8

<p>These are the tricky questions that have to be looked at suspiciously because most people assume 4 for Q2 and 3 for Q4 .</p>