Let angle ABD = y
Using the exterior angle theorem:
x+y = 2x
y=x
AD = BD = 6
Hence, AD=BD=BC=6
So St 1 is suff.
St 2 just gives you degree measures of the angles and we have no information about any of the lengths of the sides
So st 2 is insuff
For more information on exterior angle theorem check:
https://en.wikipedia.org/wiki/Exterior_angle_theorem
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
without (2)?
Source: Beat The GMAT — Data Sufficiency |
GMAT/MBA Expert
-
Ian Stewart
- GMAT Instructor
- Posts: 2623
- Location: Montreal
- Thanked: 1090 times
- GMAT Score:780
Or without using the exterior angle theorem:
-- angle ADB is 180 - 2x, because ADC is a straight line;
-- using that, angle ABD must be x, because the angles in triangle ADB must add to 180.
So triangle ADB is isosceles, and the length of AD is equal to the length of BD, which is equal to BC, since triangle BDC is isosceles. So if AD is 6, so is BC.
-- angle ADB is 180 - 2x, because ADC is a straight line;
-- using that, angle ABD must be x, because the angles in triangle ADB must add to 180.
So triangle ADB is isosceles, and the length of AD is equal to the length of BD, which is equal to BC, since triangle BDC is isosceles. So if AD is 6, so is BC.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
