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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 When a person aged 39 is added to a group of n people This topic has 5 expert replies and 1 member reply Top Member When a person aged 39 is added to a group of n people When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of n? (A) 7 (B) 8 (C) 9 (D) 10 (E) 11 Source: Veritas GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Mo2men wrote: When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of n? (A) 7 (B) 8 (C) 9 (D) 10 (E) 11 Source: Veritas Hello Mo2men. Let's see your question. In the first case we have the following: $$\frac{39+x}{n+1}=\frac{x}{n}+2\ -----\left(1\right)$$ and in the second case we have: $$\frac{15+x}{n+1}=\frac{x}{n}-1\ -----\left(2\right)$$ where x represents the sum of the ages of all n people in the group. Now, if we compute (1)-(2) we will get: $$\frac{39+x}{n+1}-\frac{15+x}{n+1}=2-\left(-1\right)$$ $$\Leftrightarrow\ \frac{24}{n+1}=3$$ $$\Leftrightarrow\ 8=n+1$$ $$\Leftrightarrow\ n=7.$$ Therefore, the correct answer is the option A. I hope it helps you. Feel free to ask me again if you have a doubt. Regards. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15385 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 Mo2men wrote: When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of n? (A) 7 (B) 8 (C) 9 (D) 10 (E) 11 Alternate approach: Let s = the original sum. New sum when a person of 39 years is added = s+39. New sum when a person of 15 years is added = s+15. Difference between the two new sums = (s+39) - (s+15) = 24. We can PLUG IN THE ANSWERS, which represent the current number of people. Let a = the original average. When the correct answer is plugged in, the difference between the two new sums = 24. D: 10 people Since a person of 39 years increases the average by 2, the new sum when a 39-year-old is added = (new number of people)(new average) = 11(a+2) = 11a+22. Since a person of 15 years decreases the average by 1, the new sum when a 15-year-old is added = (new number of people)(new average) = 11(a-1) = 11a-11. Difference between the two new sums = (11a+22) - (11a-11) = 33. The difference is TOO BIG. Eliminate D. B: 8 people Since a person of 39 years increases the average by 2, the new sum when a 39-year-old is added = (new number of people)(new average) = 9(a+2) = 9a+18. Since a person of 15 years decreases the average by 1, the new sum when a 15-year-old is added = (new number of people)(new average) = 9(a-1) = 9a-9. Difference between the two new sums = (9a+18) - (9a-9) = 27. The difference is still TOO BIG. Eliminate B. Notice the PATTERN. As the number of people gets SMALLER, the difference between the two new sums also gets smaller. Implication: For the difference between the two new sums to decrease to 24, a smaller answer choice is needed. The correct answer is A. A: 7 people Since a person of 39 years increases the average by 2, the new sum when a 39-year-old is added = (new number of people)(new average) = 8(a+2) = 8a+16. Since a person of 15 years decreases the average by 1, the new sum when a 15-year-old is added = (new number of people)(new average) = 8(a-1) = 8a-8. Difference between the two new sums = (8a+16) - (8a-8) = 24. Success! _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Last edited by GMATGuruNY on Wed Feb 14, 2018 1:28 pm; edited 1 time in total Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15385 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 Mo2men wrote: When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of n? (A) 7 (B) 8 (C) 9 (D) 10 (E) 11 I received a PM requesting that I explain how the problem can be solved with alligation. Let A = the one added person. Case 1: Average age for the first N people = x. Average age for A = 39. Average for the MIXTURE of all the people = x+2. Step 1: Plot the 3 averages on a number line, with the averages for N and A on the ends and the average for the mixture in the middle. N x----------------x+2----------------39 A Step 2: Calculate the distances between the averages. N x--------2-------x+2--------37-x------39 A Step 3: Determine the ratio in the mixture. The ratio of N to A is equal to the RECIPROCAL of the distances in red. N/A = (37-x)/ 2 Since there is only ONE added person, A=1. Substituting A=1 into N/A = (37-x)/2, we get: N/1 = (37-x)/2 2N = 37-x x = 37-2N. Case 2: Average age for the first N people = x. Average age for A = 15. Average for the MIXTURE of all the people = x-1. Step 1: Plot the 3 averages on a number line, with the averages for A and N on the ends and the average for the mixture in the middle. A 15----------------x-1----------------x N Step 2: Calculate the distances between the averages. A 15--------x-16-------x-1--------1------x N Step 3: Determine the ratio in the mixture. The ratio of A to N is equal to the RECIPROCAL of the distances in red. A/N = 1/(x-16). N/A = x-16. Since there is only ONE added person, A=1. Substituting A=1 into N/A = x-16, we get: N/1 = x-16 x = N+16. Since x=N+16 and x=37-2N, the expressions in blue are EQUAL: N+16 = 37-2N 3N = 21 N = 7. The correct answer is A. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13038 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 Mo2men wrote: When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of n? (A) 7 (B) 8 (C) 9 (D) 10 (E) 11 Source: Veritas One more solution: Let m = mean of ORIGINAL n people This means the SUM of the ages of the ORIGINAL n people = nm When a person aged 39 is added to a group of n people, the average age increases by 2 In other words: new mean (with extra person) of n+1 people = original mean + 2 Rewrite as: (nm + 39)/(n+1) = m + 2 Cross multiply to get: nm + 39 = (n + 1)(m + 2) Simplify: nm + 39 = nm + 2n + m + 2 Simplify: 39 = 2n + m + 2 Rearrange to get: 2n+ m = 37 When a person aged 15 is added instead, the average age decreases by 1 In other words: new mean (with extra person) of n+1 people = original mean - 1 Rewrite as: (nm + 15)/(n+1) = m - 1 Cross multiply to get: nm + 15 = (n + 1)(m - 1) Simplify: nm + 15 = nm - n + m - 1 Simplify: 15 = -n + m - 1 Rearrange to get: -n + m = 16 We now have the following system: 2n+ m = 37 -n + m = 16 Subtract the bottom equation from the top equation to get: 3n = 21 Solve: n = 7 Answer: A 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 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 Mo2men wrote: When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of n? (A) 7 (B) 8 (C) 9 (D) 10 (E) 11 We can let the original average = x, and thus, the original sum is nx; thus: x + 2 = (39 + nx)/(n + 1) (n + 1)(x + 2) = 39 + nx nx + x + 2n + 2 = 39 + nx x + 2n = 37 (Eq 1) and x - 1 = (15 + nx)/(n + 1) (n + 1)(x - 1) = 15 + nx nx + x - n - 1 = 15 + nx x - n = 16 x = 16 + n (Eq 2) Substituting Eq 2 into Eq 1, we have: 16 + n + 2n = 37 3n = 21 n = 7 Answer: A _________________ 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 Top Member Master | Next Rank: 500 Posts Joined 15 Oct 2009 Posted: 330 messages Upvotes: 27 Mo2men wrote: When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of n? (A) 7 (B) 8 (C) 9 (D) 10 (E) 11 Source: Veritas Not a whole lot different than the other answers, but: A= original average, therefore nA = total of ages Adding age 39 person increases average by two means: nA/(n+1) + 39/(n+1) = A+2 Adding age 15 person decreases average by 1 means nA/(n+1) + 15/(n+1) = A-1 Subtract equation two from equation one: 24/(n+1) = 3 Rearrrange: 3n+3 = 24, 3n=21, n=7, A • Free Practice Test & Review How would you score if you took the GMAT 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 • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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