sandy wrote:

Attachment:

#GREpracticequestion Which of the following statements individually provide(s).jpg

Which of the following statements

individually provide(s) sufficient additional information to determine the area of triangle ABC above?

Indicate

all such statements.

A) DBC is an equilateral triangle.

B) ABD is an isosceles triangle.

C) The length of BC is equal to the length of AD.

D) The length of BC is 10.

E) The length of AD is 10.

A) DBC is an equilateral triangle.

This means we can add the following to our diagram.

At this point, we see we have a special 30-60-90 right triangle, which is 10 TIMES larger than the base 30-60-90 right triangle

At this point, we can calculate the area of triangle ABC

Area = (base)(height)/2

= (10)(10√3)/2

= 50√3

So,

statement A is sufficient to determine the area of triangle ABC-----------------------------------

B) ABD is an isosceles triangle.

Consider these two triangles that satisfy the give conditions

Clearly, the area of triangle ABC in the TOP diagram is different from is the area of triangle ABC in the BOTTOM diagram

So, statement B is NOT sufficient to determine the area of triangle ABC-----------------------------------

Consider these two triangles that satisfy the give conditions

C) The length of BC is equal to the length of AD.

Clearly, the area of triangle ABC in the TOP diagram is different from is the area of triangle ABC in the BOTTOM diagram

So, statement C is NOT sufficient to determine the area of triangle ABC-----------------------------------

D) The length of BC is 10.

This provides enough information to calculate the area of triangle ABC

Area = (base)(height)/2

= (10)(10√3)/2

= 50√3

So,

statement D is sufficient to determine the area of triangle ABC-----------------------------------

Consider these two triangles that satisfy the give conditions

E) The length of AD is 10.

Clearly, the area of triangle ABC in the TOP diagram is different from is the area of triangle ABC in the BOTTOM diagram

So, statement E is NOT sufficient to determine the area of triangle ABCAnswer: A & D

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

Sign up for my free GRE Question of the Day emails