• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 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 ## In a certain office, the ratio of men to women is 3/4. tagged by: Gmat_mission ##### This topic has 3 expert replies and 1 member reply ### Top Member ## In a certain office, the ratio of men to women is 3/4. ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult In a certain office, the ratio of men to women is 3/4. If 10 men were added to the office, the ratio of men to women would be 7/6. How many men and women total are currently in the office? A. 18 B. 24 C. 28 D. 42 E. 52 OA=D Source: Princeton Review ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12982 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 Top Reply Gmat_mission wrote: In a certain office, the ratio of men to women is 3/4. If 10 men were added to the office, the ratio of men to women would be 7/6. How many men and women total are currently in the office? A. 18 B. 24 C. 28 D. 42 E. 52 OA=D Source: Princeton Review In a certain office, the ratio of men to women is 3/4. This tells us that, out of EVERY 7 people in the office, 3 are men and 4 are women. It also tells us that the TOTAL number of men and women currently in the office is divisible by 7 When we check the answer choices, we see that A, B and E are NOT divisible by 7 So, we can ELIMINATE A, B and E Now that we have just 2 answer choices remaining, we can just TEST the 2 remaining answer choices... If 10 men were added to the office, the ratio of men to women would be 7/6. This tells us that the NEW number of men and women in the office is divisible by 13 [since 7+6 = 13] Let's check the REMAINING answer choices. C) 28 When we add 10 to 28, we get 38 Since 38 is NOT divisible by 13, we can ELIMINATE C D) 42 When we add 10 to 42, we get 52, which IS divisible by 13 Answer: D Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12982 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 Gmat_mission wrote: In a certain office, the ratio of men to women is 3/4. If 10 men were added to the office, the ratio of men to women would be 7/6. How many men and women total are currently in the office? A. 18 B. 24 C. 28 D. 42 E. 52 OA=D Source: Princeton Review Another approach: Let M = number of men CURRENTLY in the office Let W = number of women CURRENTLY in the office In a certain office, the ratio of men to women is CURRENTLY 3/4. We can write: M/W = 3/4 Cross multiply to get: 4M = 3W Rewrite as: 4M - 3W = 0 If 10 men were added to the office, the ratio of men to women would be 7/6 So, M+10 = number of men HYPOTHETICALLY in the office We can write: (M + 10)/W = 7/6 Cross multiply to get: 6(M + 10) = 7W Expand left side to get: 6M + 60 = 7W Rewrite as: 6M - 7W = -60 How many men and women total are CURRENTLY in the office? We have the following system of equations: 4M - 3W = 0 6M - 7W = -60 Take the TOP equation and multiply both sides by 3. Take the BOTTOM equation and multiply both sides by 2. We get: 12M - 9W = 0 12M - 14W = -120 Subtract bottom equation from top equation to get: 5W = 120 Solve: W = 120/5 = 24 So, there are CURRENTLY 24 women To find the value of M, plug W = 24 into any equation. Take 4M = 3W and replace W with 24 to get: 4M = 3(24) Solve: M = 18 So, there are CURRENTLY 18 men The TOTAL number of people CURRENTLY in the office = 24 + 18 = 42 Answer: D Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### Top Member Legendary Member Joined 02 Mar 2018 Posted: 1104 messages Followed by: 2 members $$The\ ratio\ of\ men\ to\ women\ =>3:4\ =>\frac{3}{4}$$ $$If\ 10\ men\ were\ added\ ,\ ratio\ of\ men\ to\ women\ =>7:6$$ $$And\ the\ total\ number\ of\ men\ and\ omen\ working\ in\ the\ office\ is\ \frac{\left(3x+10\right)}{4x}=\frac{7}{6}$$ $$Therefore,\ \frac{\left(3x+10\right)}{4x}=\frac{7}{6}$$ $$6\left(3x+10\right)=4x\cdot7$$ $$18x+60=28x$$ $$60=28x-18x$$ $$60=10x$$ $$x=6$$ $$So,\ total=7x=7\cdot6=42\ \ \ \ \ OPTION\ D$$ ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2791 messages Followed by: 18 members Upvotes: 43 Gmat_mission wrote: In a certain office, the ratio of men to women is 3/4. If 10 men were added to the office, the ratio of men to women would be 7/6. How many men and women total are currently in the office? A. 18 B. 24 C. 28 D. 42 E. 52 OA=D Source: Princeton Review We can let 3x = the number of men and 4x = the number of women currently in the office. Thus we have: (3x + 10)/4x = 7/6 6(3x + 10) = 7(4x) 18x + 60 = 28x 60 = 10x 6 = x So there are 18 men and 24 women, or a total of 42 men and women in the office. Answer: D _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • 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

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

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

• Award-winning private GMAT tutoring
Register now and save up to \$200

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

### Top First Responders*

1 Ian Stewart 57 first replies
2 Brent@GMATPrepNow 31 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 21 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

199 posts
2 Max@Math Revolution

Math Revolution

84 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

69 posts
4 Ian Stewart

GMATiX Teacher

65 posts
5 GMATGuruNY

The Princeton Review Teacher

40 posts
See More Top Beat The GMAT Experts