<p>This is number 20 from a PSAT practice booklet ( a real college board question):</p>
<p>Points A, B, and X do not all lie on the same line. Point X is 5 units from A and 3 units from B. How many other points in the same plane as A, B, and X are also 5 units from A and 3 units from B.
(A) None
(B) One
(C) Two
(D) Four
(E) More than four</p>
<p>The answer is (B) but I
1. have no idea what the question is asking,
2. what strategy to use (backsolve, plug-in, etc...)
3. where the heck did "other points in the same plane" come from? Am I supposed to make up random points</p>
<p>And also, this was a number 11 on the same PSAT practice booklet. It was supposedly a medium question but I found it to be really difficult:</p>
<ol>
<li>The members of a school club are ordering T-shirts. There is a one time charge of $150 for artwork on the T-shirts and a $10 charge for each T-shirt ordered. If x represents the number of T-shirts oredered, which of the following represents the total cos, in dollars, per T-shirt.</li>
</ol>
<p>(A) 10 + 150x
(B) x + 15
(C) 10x + 150x
(D) 10 + 150x
-----------------
x
(E) 10x + 150x
-----------------
x </p>
<p>The answer is E but I dont understand.</p>
<p>Lol sorry for number 11, D and E, the line is supposed to mean that x is the denominator</p>
<p>for the first one you can make a graph with X at the origin, A 5 units up, b 3 units to the right. then it’s easy to see that there could only be one other point</p>
<p>for the second one, just realize that the total cost for all shirts is 10x+150. Thus (10x+150)/x would be the cost per shirt as asked.</p>
<p>First one is easy. You agree that all points 5 away from A are contained in a circle of radius 5, and that all points 3 away from B are contained in a circle of radius 3? See how many times they intersect. Circles on the same plane can only intersect at 2 points.</p>
<p>@mathphysicschem and @BassGuitar oh ok that makes sense. I see now. But thinking about it now, that’s such an easy question. Why was that categorized as a hard question (number 20)? I was thinking too deep into, thinking that there was more math involved or word choice to pay attention too. </p>
<p>@jpmac13 - One thing that I have come to realize about the SAT Math is: just because a problem is #20 doesn’t mean that it’s the hardest problem in the section. It only means that it requires the most critical/creative thinking, something that the SAT Math section emphasizes over the ACT Math section. Once you become familiar with this idea, you will be well on your way to a high score.</p>
<p>Good Luck! :)</p>