Lesson: Assumptions and Estimation on the GMAT

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Do we have answer to the problem at 3:44? Please do reply.
gmat-admin's picture

The question is an example of how students might make a good guess if they can’t solve the question.
Having said that, the correct answer is D (70 degrees). Here’s why:
Angle BAD = 20 degrees since this inscribed angle “holds” the same arc as angle BOD, and we know that the central angle must be twice the inscribed angle.
Since AB || CD, angle ADC = 20 degrees.
Finally, since angle ECD in an inscribed angle “holding” the diameter (ED), angle ECD = 90 degrees.
At this point, we know 2 of the 3 angles in a triangle (20 degrees and 90 degrees), so the third angle (x) must equal 70 degrees.

If the sides of a triangle have lengths x, y, and z, x + y = 30, and y + z = 20, then which of the following could be the perimeter of the triangle?

I. 28
II. 36
III. 42

A I only
B II only
C I and II only
D I and III only
E I, II, and III

gmat-admin's picture

We have to test each statement separately.

I. 28
This cannot be the perimeter, since sides x and y already have a sum of 30. So, the perimeter cannot be less than 30.

This allows us to eliminate A, C, D and E, since they all suggest that 28 IS a possible perimeter.

Answer: B

Hi Brent,
In this question,

I have two concerns with regards to Mitch's asnwer :
1. "The degree measurement of an inscribed angle = 1/2 the degree measurement of the intercepted arc."

I didn't came across this principle in our concept file that dealt with inscribed angles.

2. How did you assume CB to equal EB? Which is the principle applicable for the same?
gmat-admin's picture

Question link: http://www.beatthegmat.com/mgmat-geometry-t285465.html

1. Mitch uses different words to describe the rule I discuss at 2:54 of the following video: https://www.gmatprepnow.com/module/gmat-geometry/video/880

I would typically say "The central angle COE = 120 degrees," however Mitch says "Arc CAE = 120 degrees"

ASIDE: I don't believe I've ever seen an official GMAT question refer to an arc as having a measurement in degrees.

2. Since AB is the diameter, it "cuts" the circle into two IDENTICAL semicircles. Lines CB and FB create 30 degrees with AB.
Since CB and FB are lines within two IDENTICAL semicircles, then they must have equal length.

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