<p>hi there, i was just wondering how you guys would solve this problem. I did it an odd way that I am not confident in, and would like to see alternates if there are any.</p>
<p>what i did was set up the hypothetical case of x = y since x is said to be 4 and y is said to greater than 3. So one situation could be y = 4 as well. so with that as a reference point, i went through the choices and picked the one that HAD to be true, D. </p>
<p>hi yea this was kind of a tough problem, even tougher to explain. But ok I’ll try. D HAS to be true since if we look at the hypothetical case x = y that i was talking about b4. </p>
<p>x=y
4=4 was my example</p>
<p>they r saying for D, y< 3 then x not equal to 4</p>
<p>There is literally no way for a number below 3 to be equal to 4 for that hypothetical situation, so it has to be true.</p>
<p>C is quite blatantly a trick put out by the CB. At first glance it may look like the question, but it is certainly not. </p>
<p>Question is if x=4 then y>3 right?
well, C is If y >3 THEN x =4</p>
<p>That sets up the condition that y can be anything greater than 3, but x will still be 4. Mind you, x is not a constant, it is a variable. So how can y > 3, which entails an infinite number of values all be equal to 4?</p>
<p>On the other hand the question says IF x = 4, which sets up one situation with one unique value for the variable, THEN the y value must be greater than 4, but we do not have full information to come up with an equation. We just know y has to be bigger than 3. That is y i said up there x=y is just a HYPOTHETICAL situation that satisfies the given conditions.</p>
<p>This is a logic question about something called the “contrapositive”, not that the name matters. </p>
<p>The basic idea is this: start with any if-then statement. If you reverse the order, you do NOT get an equivalent statement. But if you reverse the order and also negate each part, the new statement is equivalent to the original.</p>
<p>So say this is true: If it rains, then the ball game is cancelled. </p>
<p>What else must be true? Switch the order and negate the clauses…</p>
<p>You get: If the ball game is not cancelled, it is not raining.</p>
<p>Or in this case, say this is true: If x=4 then y>3</p>
<p>What else is must be true? Switch the order and negate the clauses…</p>
<p>You get If y < 3 then x does not equal 4.</p>
<p>Btw, where does this question come from? It does not seem like the way the college board usually tests this concept…</p>
<p>I’ll post my solution a bit later, I’m heading out.</p>
<p>Also the reason you may not have seen it before is because there is not much they can do with the concept other than write analogous questions. so they probably dont use it much. After you learned the concept that pckeller said, it becomes one of those very easy questions. Thanks again pckeller.</p>
<p>Since the circle touches the x-axis at one point, and since the center is in the first quadrant, the radius is the y-axis of the center point (visualize it).</p>
<p>Center: (a, b)
Radius: r
Equation: (x-a)^2 + (y-b)^2 = r^2</p>
<p>You can see that the point (3.5, 2.5) is on the graph. Basically, once you figure out that the radius is 2.5, you move 2.5 to the left of the center (6, 2.5) and you get (3.5, 2.5).</p>
<p>Hi crazy bandit, that is a great solution. I can’t believe I didn’t see that lol, that really would have saved me some time. What I did was find out the radius was 2.5 since the circle only touches the line once, and then use the distance formula. If anyone needs me to elaborate, I would be happy to, but I think you can figure out by plugging in to the formula. In case you dont know it is distance = root(xsub1 - xsub2)^2 + (ysub1 - ysub2))</p>
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