<p>These are from the 2009 practice psat. I'm sure they're very easy, but I don't understand them!</p>
<p>18.) If x=4, then y>3.
If the statement above is true, which of the following statements must also be true?
a. if x>3, then y=4.
b. if x is not 4, then y is not 3.
c. if y>3, then x=4.
d. if y<3, then x is not 4. (answer)
e. if y<3, then x=4. </p>
<ol>
<li><p>If the average of x, x, and y is x, which of the following must also be true?
a. x=y
b. x<y c.="" x="">y (answer)
d. x=2y
e. y=2x</y></p></li>
<li><p>In the xy plane, line m is the reflection of line l across the x axis. If the intersection of lines l and m is the point (r,s), which of the following must be true?
a. r=0
b. s=0 (answer)
c. r=s
d. r=-s
e. rs=-1</p></li>
</ol>
<p>Thanks so much!</p>
<p>18)
The answer must also be true, so in this case, the direct opposite of what your given is the answer. You’re looking for an answer that will be true based on the what they have given you. At first glance, I thought C would be the answer but I realized that just because y>3, doesn’t have to mean x=4. I hope you understand what I’m trying to say, it’s kind of hard to explain haha.</p>
<p>25)Are there multiple answers? I can’t see why it can’t be A. x+x+y/3=x gives you x=y .
Sorry, can’t help you on that one.</p>
<p>28) If the lines are reflections across the x axis, they have to intersect somewhere along the x-axis, making y=0 or in this case “s”.</p>
<p>My mistake dreamday, the answer to 25 is A! I accidentally put the answer I put! Sorry. Thanks for the explanations!</p>
<p>For 18, you only know what is true if x = 4. Therefore, choices a and b are out–you don’t have any direct information about x values other than 4. </p>
<p>Next, look at the choices that specify y. We know that if x = 4, y > 3. But does this mean that if y > 3, x = 4? No. Suppose that you have a statement “If A, then B.” Logically, this does not imply “If B, then A.” “If B, then A” is the converse of the original statement “If A, then B.” Here is an example: “If it is noon, then Joe is eating.” If we know that Joe is eating, do we know that it’s noon? (No.)</p>
<p>The next choice is a modification of the original statement “If A, then B” that corresponds to the condition “Not B.” (Here B stands for y > 3. Then y < 3 is a way of saying “Not B.” Of course “Not B” could also be y is less than or equal to 3, or y = 2, or y = -10, etc.) In any event, we have not B. Could we have A, then? That’s impossible, because A implies B. Every time A occurs, B must follow. The only logical possibility for Not B is Not A as well. Choice d corresponds to this. “If Not B, then Not A” is known as the contrapositive of “If A then B.”</p>
<p>Choice e corresponds to “If Not B, then A.” But if we know that “If A, then B,” it would not make sense to suppose that A could happen, and yet B does not happen. So this is out.</p>
<p>I agree with Dreamday on 25, and think that Dreamday’s explanation of 28) is excellent.</p>
<p>18) D.</p>
<p>Logic:</p>
<p>If (statement 1) is true, then (statement 2) is true ---- If this statement is true…</p>
<p>then </p>
<p>if (statement 1) is not true, then (statement 2) is not true. -----then this statement is also true.</p>
<p>So we can apply this to this problem.
if x=4, then y>3.</p>
<p>So then if y is not greater than 3, x must also not be 4. (sorry if my explanation is fuzzy.)</p>
<p>25) A.
x+x+y/3 = x
x+x+y=3x
y=3x-2x
y=x.</p>
<p>28)</p>
<p>So have two lines, one line and another reflected across the x axis.
Since the lines are reflections of each other across the x axis, they will only meet at the x axis. – you can think about it like this, which point on the line, when reflected across the x axis, will remain in the same place - the only points that will work are the ones along the x axis(as you might see).</p>
<p>Since (r,s) is where they meet, S=0 (because y-coordinate is 0 for anypoint on the x axis)</p>
<p>Right–the contrapositive of a true statement is always true.</p>
<p>Thank you all so much! It all makes sense now.</p>