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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 ## The average age of a group of n people is 15 yrs. One more tagged by: swerve ##### This topic has 5 expert replies and 0 member replies ### Top Member ## The average age of a group of n people is 15 yrs. One more ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult The average age of a group of n people is 15 yrs. One more person aged 39 joins the group and the new average is 17 yrs. What is the value of n? A. 9 B. 10 C. 11 D. 12 E. 13 The OA is C. Source: Veritas Prep ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12822 messages Followed by: 1247 members Upvotes: 5254 GMAT Score: 770 swerve wrote: The average age of a group of n people is 15 yrs. One more person aged 39 joins the group and the new average is 17 yrs. What is the value of n? A. 9 B. 10 C. 11 D. 12 E. 13 The average age of a group of n people is 15 yrs. So, (sum of all n ages)/n = 15 Multiply both sides by n to get: (sum of all n ages) = 15n One more person aged 39 joins the group and the new average is 17 yrs. IMPORTANT: Once this 39-year-old is added to the group, the (NEW sum of ages) = 15n + 39 [We just added 39 to the old sum] Since we now have n+1 people, we can write: (15n + 39)/(n + 1) = 17 Multiply both sides by n to get: 15n + 39 = 17(n + 1) Expand right side: 15n + 39 = 17n + 17 Subtract 15n from both sides to get: 39 = 2n + 17 Subtract 17 from both sides to get: 22 = 4n Solve: n = 11 Answer: C Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our 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 25 Apr 2015 Posted: 2424 messages Followed by: 18 members Upvotes: 43 swerve wrote: The average age of a group of n people is 15 yrs. One more person aged 39 joins the group and the new average is 17 yrs. What is the value of n? A. 9 B. 10 C. 11 D. 12 E. 13 We use the formula: average = sum/number. We know that the average age is 15 years for n people. Thus, we have: average = sum/number 15 = sum/n 15n = sum We see that 15n is the sum of the ages original group of n people. But now one new person joins the group, and this personâ€™s age is 39. And now the number of people in the group is (n + 1). We know that the new average is 17. Thus, we have: sum/number = average (15n + 39)/(n + 1) = 17 15n + 39 = 17n + 17 22 = 2n 11 = n Answer: C _________________ 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 ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10124 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, We're told that the average age of a group of N people is 15 yrs and when one more person aged 39 joins the group, the new average is 17 yrs. We're asked for the value of N. This question can be solved in a number of different ways, including with a bit of 'number logic' and a little bit or arithmetic. Since the 39-year-old raises the average of the group from 15 to 17, the 39 essentially raises each age '2' years AND accounts for another '17' in the group. 39 - 17 = 22 and those 22 extra years would mean that there are 22/2 = 11 people who were ORIGINALLY in the group. Final Answer: C GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 swerve wrote: The average age of a group of n people is 15 yrs. One more person aged 39 joins the group and the new average is 17 yrs. What is the value of n? A. 9 B. 10 C. 11 D. 12 E. 13 Source: Veritas Prep $? = n$ Perfect opportunity to use the homogeneity nature of the average: $\left. \begin{gathered} \sum\nolimits_n { = 15 \cdot n} \hfill \\ 39 + \sum\nolimits_n { = \sum\nolimits_{n + 1} { = \,\,\,} 17 \cdot \left( {n + 1} \right)\,\,\,} \, \hfill \\ \end{gathered} \right\}\,\,\,\,\,39 + 15n = 17n + 17\,\,\,\,\,\,\, \Rightarrow \,\,\,\,2n = 39 - 17 = 22$ $? = \frac{{22}}{2} = 11$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2424 messages Followed by: 18 members Upvotes: 43 swerve wrote: The average age of a group of n people is 15 yrs. One more person aged 39 joins the group and the new average is 17 yrs. What is the value of n? A. 9 B. 10 C. 11 D. 12 E. 13 We can create the equation: (15n + 39)/(n + 1) = 17 15n + 39 = 17n + 17 22 = 2n 11 = n Answer: C _________________ 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. 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