SAT Question of the Day June 15 2013

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?

Roman numeral 1. Three

Roman numeral 2. Four

Roman numeral 3. Five

A.     Roman numeral 1 only

B.     Roman numeral 3 only

C.     Roman numeral 1 and Roman numeral 2 only

D.     Roman numeral 1 and Roman numeral 3 only

E.     Roman numeral 1Roman numeral 2, and Roman numeral 3

In a math question concentrated on Geometry I recommend to make a little diagram.

We have 4 lines in the plane. Exactly two of them are parallel – implying they never cross.

Now lets call these lines A and B and lets draw them parallel to the bottom of the page.

————————————————————————

————————————————————————

The remaining two lines (C and D) are not parallel to one another or to A or B.

This mean we can imagine they are forming a gigantic

\                /

   \           /

      \     /

         X

       /    \

    /          \

/                 \

Now lets move this X up.

It is clear C and D meet exactly once. C intersect A once and intersect B once. The same is true for D.

We have an option of 1+2+2 intersections.

However, if we continue to move the X up and the intersection between C and D is now overlapping one of the parallel lines we reduced two points.

We conclude there are either 5 or 3 points were the lines intersect.

30% out of 218,000 got it right – a surprisingly difficult question.

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