<ol>
<li><p>The Friends of the Library meet on the 3rd Sunday of every month. What is the latest possible day of the month that this meeting could take place?
a.20
b.21
c.22
d.23
e.24</p></li>
<li><p>If (x+y)(x^2-y^2)=0, which of the following must be true?
a. x=y
b. x=-y
c.x^2=y^2
d.x^2=-y^2
e.x^3=y^3</p></li>
</ol>
<p>Lol. I just made a thread on 20.</p>
<p>From crazybandit.
20.
(x+y)(x^2-y^2)=0 (Factor the second term.)
(x+y)(x+y)(x-y)=0 (Set each of the 3 terms equal to 0 and solve for x.)</p>
<p>Based on the three factors above, x could either be positive y OR negative y. We can’t make a definitive statement as to what x must be (since there are two distinct options). If x = y, the statement “(x+y)(x+y)(x-y)=0” is true. If x = -y, that statement is also true. So we can’t say either of them MUST be true, because it can be either one.</p>
<p>So if we square the equation of each of the possibilities, here’s what happens:
x = y becomes x^2 = y^2
x = -y becomes x^2 = y^2</p>
<p>Therefore, we can make a definitive statement that x^2 = y^2. If x = y, then that statement is true. If x = -y, then that statement is true. Therefore, the statement x^2=y^2 MUST be true, since it encompasses all possibilities. x = -y only encompasses one possibility.</p>
<ol>
<li> Assume the first of the month is on Monday. Then Sunday would be on the 7th. 2 sundays later (14 days) would be the 21st and that would be the latest time. Draw a calendar if you need to…</li>
</ol>
<p>muchos thanks.</p>