SAT Question of the Day Nov 11 Math problem

Test Preparation SAT Preparation
1

<p>COULD SOMEONE DRAW THE BELOW QUESTION AND EXPLAIN THE ANSWER PLEASE.! THANK YOU.</p>

<hr>

<p>Read the following SAT test question, then click on a button to select your answer. </p>

<p>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?</p>

<p>I. Three</p>

<p>II. Four</p>

<p>III. Five</p>

<p>(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I,II ,III and
The correct answer is D
Explanation</p>

<p>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 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 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 or points of intersection. Since you can’t obtain four points of intersection, the correct answer is I and III only.</p>

2

<p>lol, I can’t figure it out, how can the lines be arranged to intersect at 5 points?</p>

3

<p>Like this?</p>

<p>

<a href=“http://i52.■■■■■■■.com/293hx1u.png[/IMG]”>http://i52.■■■■■■■.com/293hx1u.png

</a></p>

4

<p>Well, if you want an explanation for all three…</p>

<p>It says that two lines, let’s say A and B are parallel. There are also another two lines, C and D which are not parallel [to each other].</p>

<p>First up, three points of intersection</p>

<p><a href=“http://img23.imageshack.us/img23/987/intersection3.jpg[/url]”>http://img23.imageshack.us/img23/987/intersection3.jpg&lt;/a&gt;&lt;/p&gt;

<p>Read carefully. The problem only states that C&D are not parallel to each other, so lines C or D can be parallel to A & B. If either line C or line D(NOT both) is parallel to A & B, you’ll end up with three lines of intersection, so this is a yes.</p>

<p>Then, four points…</p>

<p><a href=“http://img600.imageshack.us/img600/6595/fourpointsofintersectio.png[/url]”>http://img600.imageshack.us/img600/6595/fourpointsofintersectio.png&lt;/a&gt;&lt;/p&gt;

<p>The only way to have exactly four points of intersection is to have two sets of parallel lines; A||B and C||D. However, given the problem, lines C and D are NOT parallel. Therefore, four is not a number of points where at least two of the lines intersect.</p>

<p>And, of course, five points.</p>

<p><a href=“http://img84.imageshack.us/img84/1310/fivepointsintersection.png[/url]”>http://img84.imageshack.us/img84/1310/fivepointsintersection.png&lt;/a&gt;&lt;/p&gt;

<p>If both lines C and D are not parallel to each other, and both are not parallel to A and B, there will be five points of intersection ( A&C, A&D, B&C, B&D, and C&D). So yes.</p>

<p>Answer is D, 3 points and 5 points</p>

5

<p>^Actually, your diagram for 3 points of intersection has 3 parallel lines, which isn’t allowed. However, 3 points of intersection are still possible. Think of 2 parallel lines and 2 diagonal ones making one triangle.</p>