BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

The figure shows the right triangle ABC and inscribed circle, which is tangential at D. AD

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

The figure shows the right triangle ABC and inscribed circle, which is tangential at D. AD

by Max@Math Revolution » Fri Mar 27, 2020 12:50 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

[GMAT math practice question]

The figure shows the right triangle ABC and inscribed circle, which is tangential at D. AD = p and CD = q. What is the area of ABC?
3.27DS.png
1) p = 2, q = 3.
2) The radius of the inscribed circle is 1.
Top
Source: — Data Sufficiency |
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

Re: The figure shows the right triangle ABC and inscribed circle, which is tangential at D. AD

by Max@Math Revolution » Sun Mar 29, 2020 9:36 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

=>
3.27ds(a).png
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

We can put BC = BF = x.
Put BC = a = q + x, AC = b = p + q and AB = c = p + x.
Then the area of triangle ABC = (1/2)ac and x = (a-b+c)/2, p = (b-(a-c))/2 and q = (b+(a-c))/2
Then we have
pq = {(b-(a-c))/2}{(b+(a-c))/2}
pq = {b^2 + b(a-c) – b(a-c) - (a-c)2}/4
pq = (b^2 – (a-c)2)/4
pq = {b^2 – (a-c)(a-c)}/4
pq = {b^2 – (a2 – ac – ac + c2)}/4
pq = (b^2 - a2 - c2 + 2ac)/4
pq = ac/2.
Thus, the area of the triangle ABC is pq, and condition 1) is sufficient.

Condition 2)

Since there are a lot of possibilities for p and q, condition 2) does not yield a unique solution, and it is not sufficient.

Therefore, A is the answer.
Answer: A
Top
Post new topic Post Reply
• Page 1 of 1