Q25

[jiyoonsim]

This was tough passage to disect. Can anyone help me out with the question #25 and #27 please? I think I got most of the opinion/tone questions right, but failed the detail questions.

For #25 my answer was D, and for 27 I picked C.

[giladedelman]

Thanks for your post! I agree, this is a pretty dense passage.

Question 25 is irritating because we have to look out for four correct inferences and one incorrect inference.

(A) is the correct answer because the passage does not support the idea that the total number of protrusions in the Koch curve depends on the length of the initial line. In fact, it suggests the exact opposite: the protrusions are formed by taking a certain portion (a third) of the line segment, so the length is irrelevant.

(B) is incorrect it is a valid inference. At each stage of the Koch curve, you're taking a line segment and changing it into four segments each one third the length of the original.

(C) is supported in lines 27-31: "Theoretically, the Koch curve is the result of infinitely many steps in the construction process, but the finest image approximating the Koch curve will be limited by the fact that eventually the segments will get too short to be drawn or displayed."

(D) is supported because we're told that each phase of the curve is constructed by taking your line segment and making it into four equal parts. (You go from ____ to _/\_.)

(E) is supported because the length of each line segment is one third the length of the segment in the stage before it, so its length depends on the length of the preceding segment, all the way back to the beginning.

Question 27 is also an inference question. We're looking for a statement with concrete support in the text.

(D) is correct because the passage describes the development and applications of fractal theory at great length, but tells us that "an exact definition of fractals has not been established." So you can have development and applications even before having a precise definition.

(A) is unsupported. We aren't told that the appeal is limited in any particular way.

(B) is out of scope; the passage doesn't address recent breakthroughs in mathematical theory.

(C) sort of resembles what the pro-fractal crowd says, but they never actually say that fractal geometry can replace traditional geometry; nor does engineering come up.

(E), on the other hand, sort of leans to the anti-fractal crew, but again, the passage never lays out the requirements for "enthusiastic support among a significant number of mathematicians." So there's no support for this.

Did that clear these up for you? Let me know if you still have questions.

[GodLovesUgly]

If anyone could clarify this that would be great. I am wondering why we would eliminate (A)? We are obviously looking for the one choice that CANNOT be inferred from the passage, but how can (A) not be inferred?? If you start with a longer initial line segment, the resulting figure or shape will be larger, longer, etc., right? Maybe I am missing something? Thanks for the help...

[pewals13]

I think the key to eliminating (A) is the qualifier "at any stage." The length of the initial line doesn't impact the number of protrusions because they are created based on proportion. You can continually break each line segment into thirds indefinitely, theoretically.

So whether the line you start out with is as big as the Empire State Building, or as small as an ant, the second stage will always involve one protrusion, and the third will always involve four protrusions, and so on.

[bswise2]

I chose D because I read it as saying that all the line segments composing the Koch curve are of equal length. The AC ambiguously refers to it as it, which, in my opinion, could be referring the the previously mention Koch curve just as much as it could be referring to "every stage." That's why I chose D. Any tips on this? I fear that I would still read it the same way if faced with this question again...

[IrisH894]

A is wrong because the total number of protrusions only depends on the stage it is at.
For example, in the first stage you get one protrusion, in the second stage 4 protrusions, in the third stage 16 protrusions, and so on.
It has nothing to do with the length of the initial line, or the length of the segments.

E is right because the length of the line segments at any stage of the construction only depends on two variables: the length of the initial line, and the number of stages it has gone through. I think the equation is: segment length = initial length/ 4 to the nth power (n being the number of stage it's at)