GMATPrepNow wrote:

SajjadAhmad wrote:

What is the maximum number of points common to the intersection of a square and a triangle if no two sides coincide?

(A) 4

(B) 5

(C) 6

(D) 8

(E) 9

We might start by examining the number of ways that ONE SIDE of a triangle can intersect a square.

In other words, in how many ways can a LINE intersect a square?

After a bit of mental imagery, we might conclude that a SINGLE LINE can intersect a square

in at MOST 2 waysA triangle is composed of THREE LINE SEGMENTS.

If each SINGLE LINE can intersect a square

in at MOST 2 ways, then the 3-sided triangle can intersect a square in AT MOST 6 ways (with 2 intersections per line)

So, the correct answer must be

6 or lessAt that point, if we're able to sketch a scenario in which there are 6 intersections, we can be certain that this is, indeed, the GREATEST number of intersections.

Answer:

Cheers,

Brent

GMATPrepNowBrent, I did exactly that which you describe. I concluded similarly that

**Quote:**

If each SINGLE LINE can intersect a square in at MOST 2 ways, then the 3-sided triangle can intersect a square in AT MOST 6 ways (with 2 intersections per line).

Then, however, you write, "

if we're able to sketch a scenario in which there are 6 intersections," our calculation is correct.

It sounds as if the outcome depends on whether or not the maximum number intersection points we have calculated can be

drawn. Is that impression accurate?

If not, may we assume that, for two co-planar shapes without concave sides, the maximum number of intersection points can be calculated by taking the figure with fewer sides "S," and multiplying S by two? (If same S, use S.)

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