November 22, 2018 November 22, 2018 10:00 PM PST 11:00 PM PST Mark your calendars  All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA) November 23, 2018 November 23, 2018 10:00 PM PST 11:00 PM PST Practice the one most important Quant section  Integer properties, and rapidly improve your skills.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 12 Dec 2012
Posts: 151
Location: Poland

Three sisters have an average (arithmetic mean) age of 25 ye
[#permalink]
Show Tags
Updated on: 15 Dec 2016, 14:35
Question Stats:
69% (01:19) correct 31% (01:28) wrong based on 246 sessions
HideShow timer Statistics
Three sisters have an average (arithmetic mean) age of 25 years and a median age of 24 years. What is the minimum possible age, in years, of the oldest sister? (A) 24 (B) 25 (C) 26 (D) 27 (E) 28 f = age of the first sister, etc. M = Median = 24 m = mean
\(\frac{f+s+t}{3}=25=m\)
\(M=s=24\)
\(f+s=51\)
My assumption: The problem says about the oldest sister, so I assumed that:
f≤s<t
In case the younger sisters were twins. The book explains: The youngest sister must be less than or equal to 24 years old. Agreed.
However, the book also assumes that:
s≤t:
Of course, the oldest sister must be at least as old as the middle sister (...) Not agreed. (Further implications concerning M=24 that turn the ≤ into the < possibility are correct.)
My thinking is: If there is one sister that is the oldest, she must not be the same age as the younger sister(s). Hypothetically, she could be 9 months older and still born in the same year, but I think it is impossible from the medical point of view. Or the sisters could be a step sisters, etc. Nevertheless, this situation is purely hypothetical and  even if the point was to mislead the thinker  in my opinion this is a bit too much, because the very natural assumption for expression of an age is it be an integer.
Moreover, if there were a hypothetical sets:
A={24,25,25}, OR B={25,25,25},
none of the elements in each set were the greatest (oldest), because "the greatest" is an expression inherently relative to some other objects.
Disputably, in the A'={24,25} we could point 25 as "the greatest", because it's the greatest within the set, even though inside the set it is only "the greater" element, because there is only one other element to be relatively smaller (24).
If you have a one brother, you never say "I am his oldest brother" (unless you're joking). Instead, you will say: "I am his older brother.". Ain't right?
And if you have two siblings, you will say: "I am the oldest one (of us three).", won't you? Source: Manhattan Advanced GMAT Quant
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
If I answered your question with this post, use the motivating power of kudos!
Originally posted by HumptyDumpty on 14 Jan 2013, 05:16.
Last edited by stonecold on 15 Dec 2016, 14:35, edited 1 time in total.
OE Hidden



Manager
Joined: 18 Oct 2011
Posts: 87
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01302013
GPA: 3.3

Re: Three sisters have an average (arithmetic mean) age of 25 ye
[#permalink]
Show Tags
15 Jan 2013, 08:32
This question is fairly simple. Note that in the question stem they do not say that each sister has a different age..meaning two could have the same age. If we have a median of 24 that means the middle sister is 24. If we have a mean of 25 that means that the total age of all 3 sisters is 75. If you take out the middle sisters age from the total you get 51...the youngest and oldest sisters must combine for 51 years. The first answer choice that makes sense is 27 years for the oldest sister leaving the middle and youngest to be 24.



Manager
Joined: 12 Dec 2012
Posts: 151
Location: Poland

Re: Three sisters have an average (arithmetic mean) age of 25 ye
[#permalink]
Show Tags
15 Jan 2013, 08:59
Dear sambam, Quote: This post is about a doubtful assumption, perhaps an error in the book, which however doesn't influence the answer to the original question. Solving the problem as such is not the purpose of my post. I would be glad if you've read the whole story before answering .
_________________
If I answered your question with this post, use the motivating power of kudos!



Current Student
Joined: 12 Aug 2015
Posts: 2632

Three sisters have an average (arithmetic mean) age of 25 ye
[#permalink]
Show Tags
15 Dec 2016, 14:38
Nice Question. Here is my Solution to this one >
Let the Age of the three sister in ascending order be > S1 S2 S3
Mean = 25
\(Using Mean =Sum/#\)
Sum(3)=25*3=75
Hene S1+S2+S3=75
As #=3=Odd => Median = 2nd term = S2 S2=24
Now to minimise the largest term that is S3 we must maximise all other terms. S1=S2=24
Hence 2*24+S3=75 S3=7548=27
Hence D
_________________
MBA Financing: INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)AVERAGE GRE Scores At The Top Business Schools!



Manager
Joined: 13 Dec 2013
Posts: 158
Location: United States (NY)
Concentration: General Management, International Business
GMAT 1: 710 Q46 V41 GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)

Re: Three sisters have an average (arithmetic mean) age of 25 ye
[#permalink]
Show Tags
20 Dec 2016, 03:40
The median is 24, which means that the age of the middle sister must be 24. So we have x, 24, y, where x is the age of the youngest sister and y is the age of the oldest sister. To find the minimum age of the oldest sister the other values should be maximized. We also know that the sum of all three ages is 75. Setting x as 24 (the highest value it can be if the median is 24) gives y as 27.
POE for AC:
A) x must be 24 or lower (for 24 to be the mean). If y is 24 the sum of 75 cannot be met. B) x must be 24 or lower (for 24 to be the mean). If y is 25 the sum of 75 cannot be met. C) x must be 24 or lower (for 24 to be the mean). If y is 26 the sum of 75 cannot be met.



Director
Joined: 26 Oct 2016
Posts: 640
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: Three sisters have an average (arithmetic mean) age of 25 ye
[#permalink]
Show Tags
28 Feb 2017, 05:45
Posting official solution of this problem.
Attachments
official_average.PNG [ 118.79 KiB  Viewed 1147 times ]
_________________
Thanks & Regards, Anaira Mitch



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4230
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: Three sisters have an average (arithmetic mean) age of 25 ye
[#permalink]
Show Tags
28 Feb 2017, 07:51
HumptyDumpty wrote: Three sisters have an average (arithmetic mean) age of 25 years and a median age of 24 years. What is the minimum possible age, in years, of the oldest sister?
(A) 24 (B) 25 (C) 26 (D) 27 (E) 28 a + b + c = 75 Given  a + 24+ c = 75 Now, a + c = 51 Now comes the fun part, so check using options... Here C is the oldest sister, and we need to minimize c by maximizing a.. (A) If c = 24 , a = 27 ( not Possible as a > c ) (B) If c = 25 , a = 26 ( not Possible as a > c ) (C) If c = 26 , a = 25 ( not Possible as a > b < c )(D) If c = 27 , a = 24 ( possible as a ≤ b < c )(E) If c = 28 , a = 23 ( Possible as but now, this is not the minimum value c can take )Hence, answer must be (D) 27
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: Three sisters have an average (arithmetic mean) age of 25 ye
[#permalink]
Show Tags
02 Mar 2017, 17:10
HumptyDumpty wrote: Three sisters have an average (arithmetic mean) age of 25 years and a median age of 24 years. What is the minimum possible age, in years, of the oldest sister?
(A) 24 (B) 25 (C) 26 (D) 27 (E) 28 Since 3 sisters have an average age of 25 years, the sum of their ages is 75. Since the median is 24, the two youngest sisters could both be 24 years old. Thus, the minimum possible age of the oldest sister is 75  (24 + 24) = 75  48 = 27. Answer: D
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



NonHuman User
Joined: 09 Sep 2013
Posts: 8872

Re: Three sisters have an average (arithmetic mean) age of 25 ye
[#permalink]
Show Tags
27 Aug 2018, 03:02
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: Three sisters have an average (arithmetic mean) age of 25 ye &nbs
[#permalink]
27 Aug 2018, 03:02






