Wednesday, March 07, 2007

SAT Question

For lack of any decent blog material, and because we're all about as lethargic as a bunch of meth-heads hocked up on OxyContin, I thought I'd share this highschool level brain buster.

Four distinct lines lie in a plane, and exactly two of them are parallel. Which of the following could be the number of points where at least two of the lines intersect?

  1. Three
  2. Four
  3. Five
  1. click to choose answer A I only
  2. click to choose answer B III only
  3. click to choose answer C I and II only
  4. click to choose answer D I and III only
  5. click to choose answer E I, II, and III

3 Comments:

Blogger Garble said...

This comment has been removed by the author.

7/3/07 17:04  
Blogger Garble said...

3, 4, 5

7/3/07 17:04  
Blogger Jim Brannick said...

Garbs, you're wrong (both times). The correct answer is choice "D" (3 and 5). Here's why:
Since exactly two of the four lines are parallel, the other two lines are not parallel. If the two non-parallel lines intersect at a point that is not on either one of the parallel lines, then the configuration of lines will give a total of 5 points of intersection. (The best way to verify this is by drawing the two parallel lines and then putting in the other two lines.) If, on the other hand, the two non-parallel lines intersect at a point that is on one of the parallel lines, then there will be a total of 3 points of intersection in the figure. (Again, a sketch is the best way to verify this.) Any arrangement of the four lines will again yield either 3 or 5 points of intersection. Since you can’t obtain four points of intersection, the correct answer is I and III only.
If it's any consolation Garble, the SAT website classified that question as "hard".

8/3/07 06:13  

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