Data Sufficiency

If AB || DE, and AB = 10, what is the length of DE?

(1) BC = 6 and CE = 4
(2) DC = 3 and CB = 6

Answer: B
Difficulty level: 650 - 700
Source: www.gmatprepnow.com

Brent@GMATPrepNow wrote:

If AB || DE, and AB = 10, what is the length of DE?

(1) BC = 6 and CE = 4
(2) DC = 3 and CB = 6

Answer: B
Difficulty level: 650 - 700
Source: www.gmatprepnow.com

Let's first add the given information (and their implications) to the diagram

If AB || DE, we know that ∠BAC = ∠CED and ∠ABC = ∠DCE
Also, since vertically opposite angles are equal, we know that ∠ACB = ∠DCE



Now that we've identified 3 pairs of EQUAL angles, we can conclude that the two triangles are SIMILAR
So, we need to determine which sides are corresponding.
Notice that side AB and side DE BOTH lie between the angles denoted by a star and a square.
This means that side AB corresponds with side DE (denoted by BLUE lines)


Likewise, side BC and side CD both lie between the angles denoted by a circle and a square.
This means that side BC corresponds with side CD (denoted by RED lines)


Finally, side AC and side CE both lie between the angles denoted by a circle and a star.
This means that side AC corresponds with side CE (denoted by GREEN lines)


Now onto the question!!!!

Target question: What is the length of DE?

Statement 1: BC = 6 and CE = 4
Add this info to the diagram:


Notice that we don't know the lengths of two corresponding sides.
As such, we can't determine the magnification factor of the two similar triangles (see the video below for more information about magnification factor)
As such, there's no way to determine the length of side DE
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: DC = 3 and CB = 6
Add this info to the diagram:

Notice that DC and CB are corresponding sides.
So, the magnification factor of the similar triangles = 6/3 = 2
In other words, ∆ABC is 2 times the size of ∆EDC
So, if side AB = 10, then side DE (the side that corresponds with side AB) must have length 5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

RELATED VIDEO FROM OUR COURSE
https://www.youtube.com/watch?v=c2sNcDDhUSQ