• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Each person in a room attends exactly one of the three tagged by: M7MBA ##### This topic has 1 expert reply and 0 member replies ## Each person in a room attends exactly one of the three Each person in a room attends exactly one of the three colleges A, B, and C. What is the probability that a person selected at random from the people in the room attends college B? (1) The number of people in the room attending college B is 20 less than the sum of the numbers of people in the room attending colleges A and C. (2) The ratio of the number people in the room attending college B to the sum of the numbers of people in the room attending colleges A and C is 2 to 3. The OA is B. I don't know how to use the statement (2) to get an answer. Can you help me here experts? Thanks, ### GMAT/MBA Expert Legendary Member Joined 20 Jul 2017 Posted: 503 messages Followed by: 10 members Upvotes: 86 GMAT Score: 770 The question stem gives that the total number of people in the room is A + B + C. We want to find the probability that one person selected from this total attends college B. In other words, we want to find $$\frac{B}{A+B+C}$$ Statement 1 tells us that $$B=A+C-20$$ $$B+20=A+C$$ Plugging in B+20 in for A+C in our initial fraction gives $$\frac{B}{B+B+20}$$ $$\frac{B}{2B+20}$$ At this point, we have no idea what the value of B is - if B = 10, then the probability will be 10/40=1/4; if B = 30, then the probability will be 30/80=3/8. So we can't solve definitively for the probability of selecting someone from college B. Insufficient. Statement 2 tells us that $$\frac{B}{A+C}=\frac{2}{3}$$ $$\frac{3}{2}B=A+C$$ Plugging (3/2)B in for A+C in our initial fraction gives $$\frac{B}{B+\frac{3}{2}B}$$ $$\frac{B}{\frac{5}{2}B}$$ $$\frac{1}{\frac{5}{2}}$$ $$\frac{2}{5}$$ So the probability of picking a student from college B is 2/5. Sufficient. _________________ Erika John - Content Manager/Lead Instructor https://gmat.prepscholar.com/gmat/s/ Get tutoring from me or another PrepScholar GMAT expert: https://gmat.prepscholar.com/gmat/s/tutoring/ Learn about our exclusive savings for BTG members (up to 25% off) and our 5 day free trial Check out our PrepScholar GMAT YouTube channel, and read our expert guides on the PrepScholar GMAT blog • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for \$0

Available with Beat the GMAT members only code

### Top First Responders*

1 Brent@GMATPrepNow 64 first replies
2 fskilnik@GMATH 58 first replies
3 Jay@ManhattanReview 46 first replies
4 GMATGuruNY 34 first replies
5 Rich.C@EMPOWERgma... 24 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 fskilnik@GMATH

GMATH Teacher

120 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

99 posts
3 Max@Math Revolution

Math Revolution

88 posts
4 Jay@ManhattanReview

Manhattan Review

82 posts
5 Rich.C@EMPOWERgma...

EMPOWERgmat

65 posts
See More Top Beat The GMAT Experts