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Line DB divides Rectangle ABCD into two equal triangles. Is

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by BTGmoderatorDC » Sun Dec 09, 2018 2:03 am

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Answers

A

B

C

D

E

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Difficulty—

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Line DB divides Rectangle ABCD into two equal triangles. Is Angle ABD equal to 30 degrees.

(1) One side of Triangle ABD is equal to 2.

(2) One side of Rectangle ABCD is 1.

OA E

Source: Veritas Prep
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Sun Dec 09, 2018 9:05 pm
BTGmoderatorDC wrote:Image

Line DB divides Rectangle ABCD into two equal triangles. Is Angle ABD equal to 30 degrees.

(1) One side of Triangle ABD is equal to 2.

(2) One side of Rectangle ABCD is 1.

OA E

Source: Veritas Prep
Needless to say that each statement alone is not sufficient.

Combining both the statements:

Case 1: Say AB = 1 and AD = 2, then we have /_A = 90º, and angle B can be determined. Let's not calculate it as of now.
Case 2: Say DB = 2 and AD = 1, then we have /_A = 90º, and angle B can be determined. Let's not calculate it as of now.

Note that the value of and B would be different from both the cases, thus, no unique value. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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by swerve » Mon Dec 10, 2018 9:25 am
Hi,

I had a very basic doubt here.

If a line divides a rectangle into two equal triangles, shouldn't this line be the rectangle's diagonal and create a 45-degree angle at the vertices?
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by GMATGuruNY » Mon Dec 10, 2018 9:28 am
swerve wrote:Hi,

I had a very basic doubt here.

If a line divides a rectangle into two equal triangles, shouldn't this line be the rectangle's diagonal and create a 45-degree angle at the vertices?
Yes, the line will be a diagonal, but the four angles created by this diagonal will each be 45 degrees only if the rectangle is a square.
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by Brent@GMATPrepNow » Mon Dec 10, 2018 9:29 am
swerve wrote:Hi,

I had a very basic doubt here.

If a line divides a rectangle into two equal triangles, shouldn't this line be the rectangle's diagonal and create a 45-degree angle at the vertices?
IF all 4 sides of the rectangle have EQUAL length (i.e,, the shape is a square), then the diagonal will create two 45-45-90 right triangles.
However, if the sides are not all the same length, the resulting triangles will NOT be 45-45-90 right triangles.

Cheers,
Brent
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