Thanks, pemdas - and, cans, to add to that... the problem with C isn't the "both statements together are sufficient" portion, it's the "but NEITHER ALONE" portion. Yes, knowing two points on the same line will give you the slope, but actually statement 1 ALONE is sufficient. The fact that the circle is centered on (0,0) and that our line is tangent to that circle at (2,0) means that our line runs perpendicular to the x-axis. We can now draw that line...it's x = 2. We don't need any more information, so we don't need to bring in statement 2 (to get C) - we already have all the information we need with statement 1 alone.
And, sl750 - that's why I bring up that you can play one statement off of the other. It's a step above in terms of strategy...think of it this way:
1) When assessing statement 2, DO NOT include the information you learned from statement 1. Remember, choice B is "Statement 2 ALONE"...you need to have a full read on statement 2 independent of any other information.
BUT
2) Statement 2 doesn't exist in a vacuum. It's part of a larger question, which the author wrote in very carefully-chosen terms. Therefore, statement 1 can provide you with some clues that will be helpful in independently assessing statement 2. Consider, for example, the question:
What is the value of x?
(1) x is positive
(2) x^2 = 25
Hopefully this is a pretty basic example, but pay attention to the lesson. You DO NOT want to assess statement 2 with the idea that x is positive. You'd get this question wrong if you did that...while looking at statement 2 we only know that x^2 = 25. But say you were to take the square root of 25 and say that x = 5. Now you really should look back at statement 1, which says that x is positive. Do you need that information? Or does statement 2 on its own guarantee that information? Had you forgotten about the potential for x to be -5 (based on x^2 = 25), statement 1 can remind you that you need to explicitly make that decision... "Do I need an extra statement to tell me that x is positive?". That should encourage you to ask "based on statement 2, could x be negative?". And it can, so having looked at statement 1 before making a final determination on statement 2, you can save yourself from a bad answer.
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On this coordinate question, I think that looking at statement 2 before you finalize your answer on statement 1 can be instrumental in getting the right answer. If all you take from statement 1 is that "the line goes through (2,0)", then you'd say "Not Sufficient". But looking at statement 2, which gives you a second point and is similarly not sufficient, that should give you pause. C is a gift answer here...two statements each give you one point so together you can take (y1 - y2)/(x1 - x2) and you have your slope, quickly. That should raise a flag in your mind - why was C so obvious? What am I missing? And since statement 1 has more information ("tangent at point 2,0") than statement 2 ("runs through point 3,4"), then you most likely want to double-check statement 1 through the lens of "wait, do I really need them to tell me statement 2?".
I think of it like a chess match - there are two dimensions here when you see an opponent pick up a piece, move it to a square, ponder the move, then take it back. You're not at all "wrong" if you ignore that move and just play based on where the pieces are on the board. But you're a better player and more likely to win if you think about what the opponent was setting up by thinking about that move. Even though that move doesn't exist officially, you know that it's in your opponent's move...he may be trying to defend his queen or hoping to attack your back line. Knowing what's on his mind can help you think a few moves ahead.
Well, considering the POTENTIAL (but not actual) impact of "the other" statement in DS is the same thing. Yeah, you don't know statement 2 yet when you're reading statement 1. But the author of the question wrote both and the question format allows you to take a sneak peak at statement 2 before you make your final decision on statement 1, so why not give it a look to see if you can get inside the head of the author?
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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