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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 ## Sarah is in a room with 6 other children. If the other child ##### This topic has 2 expert replies and 0 member replies ### Top Member ## Sarah is in a room with 6 other children. If the other child ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Sarah is in a room with 6 other children. If the other children are 2, 4, 5, 8, 10, and 13 years old, is Sarah 7 years old? (1) The age of the fourth oldest child is equal to the average (arithmetic mean) of the seven childrenâ€™s ages. (2) Sarah is not the oldest child in the room. OA C Source: Manhattan Prep ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1975 messages Followed by: 30 members Upvotes: 470 Top Reply BTGmoderatorDC wrote: Sarah is in a room with 6 other children. If the other children are 2, 4, 5, 8, 10, and 13 years old, is Sarah 7 years old? (1) The age of the fourth oldest child is equal to the average (arithmetic mean) of the seven childrenâ€™s ages. (2) Sarah is not the oldest child in the room. OA C Source: Manhattan Prep Given: Ages of 6 children 2, 4, 5, 8, 10, and 13 years We have to determine whether Sarah is 7 years old. Let's take each statement one by one. (1) The age of the fourth oldest child is equal to the average (arithmetic mean) of the seven childrenâ€™s ages. Case 1: Say Sarah is 7 years old. Ages of 7 children arranged in ascending order: 2, 4, 5, 7, 8, 10, 13. The age of the fourth oldest child = 7 Average of the ages of the 7 children = (2 + 4 + 5 + 7 + 8 + 10 + 13)/7. The answer is yes. Case 2: Say Sarah is x years old, where x > 7. Ages of 7 children arranged in ascending order: 2, 4, 5, 8, 10, 13, x. The age of the fourth oldest child = 8 Average of the ages of the 7 children = (2 + 4 + 5 + 8 + 10 + 13 + x)/7 = 8 => (42 + x)/7 = 8 => x = 14. The answer is No. No unique answer. Insufficient. (2) Sarah is not the oldest child in the room. Certainly insufficient. This Statement means that Sarah's age < 13. Still many possible ages of Sarah. Insufficient. (1) and (2) together From (1) and (2), we find that Case 2 discussed in Statement 1 is invalid. Let's see if Sarah can be less than 7 years. Case 3: Say Sarah is x years old, where x < 7. Ages of 7 children arranged in ascending order: x, 2, 4, 5, 8, 10, 13. The age of the fourth oldest child = 5 Average of the ages of the 7 children = (x + 2 + 4 + 5 + 8 + 10 + 13)/7 = 5 => (42 + x)/7 = 5 => x = -7. This is not possible since x must be a nonnegative number. Thus, x = Sarah's age = 7. Sufficient. The correct answer: C Hope this helps! -Jay _________________ Manhattan Review Locations: Manhattan Review Madhapur | GMAT Prep Kukatpally | GRE Prep Jayanagar | Tarnaka GRE Coaching | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15348 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 Top Reply Quote: Sarah is in a room with 6 other children. If the other children are 2, 4, 5, 8, 10, and 13 years old, is Sarah 7 years old? (1) The age of the fourth oldest child is equal to the average (arithmetic mean) of the seven childrenâ€™s ages. (2) Sarah is not the oldest child in the room. Let S = Sara's age. Sum of the ages = 2+4+5+8+10+13+S = 42+S. Statement 1: Since the average age is equal to an INTEGER -- the fourth largest age -- we get: Sum of the ages = (number of ages)(average age) = (7)(INTEGER) = multiple of 7. The blue expression and the red expression each represent the sum of the ages and thus are EQUAL: 42+S = (multiple of 7) S = (multiple of 7) - 42 S = (multiple of 7) - (multiple of 7) S = multiple of 7. Case 1: S=7, with the result that the ages are 2, 4, 5, S=7, 8, 10, 13 Since the average age must be equal to the fourth largest -- 7 -- we get: Sum of the ages = (number of ages)(average age) = 7*7 = 49. Since the sum of the ages = 42+S, we get: 42+S = 59 S=7. This works. Case 2: S>7, with the result that the ages are 2, 4, 5, 8, 10, 13, Sâ‰Ą14 Since the average age must be equal to the fourth largest -- 8 -- we get: Sum of the ages = (number of ages)(average age) = 7*8 = 56. Since the sum of the ages = 42+S, we get: 42+S = 56 S=14. This also works. Thus, Statement 1 allows for two cases: Case 1: S=7 Case 2: S=14 Since the answer to the question stem is YES in Case 1 but NO in Case 2, INSUFFICIENT. Statement 2: Since S cannot be the oldest, S<13. If S=7, then the answer to the question stem is YES. If S=1, then the answer to the question stem is NO. INSUFFICIENT. Statements combined: Of the two options for S in Statement 1, only S=7 is such that S<13. Thus, S=7, with the result that the answer to the question stem is YES. SUFFICIENT. The correct answer is C. _________________ 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! 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