Jun 19 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Jun 22 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jun 23 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes. Jun 24 10:00 PM PDT  11:00 PM PDT Take 20% off the plan of your choice, now through midnight on Monday, 6/24
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55706

The twelve numbers shown represent, the ages, in years, of the twelve
[#permalink]
Show Tags
20 May 2019, 21:20
Question Stats:
83% (01:30) correct 17% (01:27) wrong based on 35 sessions
HideShow timer Statistics
FRESH GMAT CLUB TESTS QUESTION x, x, x, x, 8, 8, 8, 8, 12, 12, 11,y The twelve numbers shown represent, the ages, in years, of the twelve children in a school bus. What is the median age, in years, of the twelve children in the bus? (1) x = 10 (2) y = 13
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



ISB School Moderator
Joined: 08 Dec 2013
Posts: 432
Location: India
Concentration: Nonprofit, Sustainability
WE: Operations (NonProfit and Government)

Re: The twelve numbers shown represent, the ages, in years, of the twelve
[#permalink]
Show Tags
20 May 2019, 21:32
Bunuel wrote: FRESH GMAT CLUB TESTS QUESTION x, x, x, x, 8, 8, 8, 8, 12, 12, 11,y The twelve numbers shown represent, the ages, in years, of the twelve children in a school bus. What is the median age, in years, of the twelve children in the bus? (1) x = 10 (2) y = 13 Median is the middlemost number when a list is arranged in ascending order, for even number of elements the median is the mean of two middlemost numbers/ Statement 1: Y 8 8 8 8 Y 10 10 10 10 Y 11 Y 12 Y; Y represent the positions where we can put y (Y age in years so integer) When Y<8 median is 10 When Y >12 median is 10 When y=10/11 median is still 10 When y= 9, median still 10. So sufficient. Statement 2. y=13 x, x, x, x, 8, 8, 8, 8, 11, 12, 12, 13; median= 8.5 for x<=8 But for x=10 we saw that median is 10. So B statement is insufficient. Only A.
_________________
Kindly drop a '+1 Kudos' if you find this post helpful.GMAT Math Book I never wanted what I gave up I never gave up what I wanted



CrackVerbal Quant Expert
Joined: 23 Apr 2019
Posts: 15

Re: The twelve numbers shown represent, the ages, in years, of the twelve
[#permalink]
Show Tags
22 May 2019, 02:16
This a perfect question that we can use the concept of maximization and minimization. There are three things to keep in mind while solving questions related to the median :
1. By definition, the median is the middle value in a list of numbers arranged in ascending or descending order. 2. The arrangement is always key to solving questions related to the median. 3. On questions where we have a list of elements with many variables, maximization and minimization is the best way to proceed.
Now lets jump into the solving of the question.
We have the list x, x, x, x, 8, 8, 8, 8, 12, 12, 11,y. Since the data here are of ages, x and y have to be integers.
Statement 1 : x = 10
Arranging the elements in ascending order we get, 8, 8, 8, 8, 10, 10, 10, 10, 11, 12, 12, y.
Now let us think about the max and min values of y. If y >= 12, then the max median will be 10. If y <= 12, then the list now becomes y, 8, 8, 8, 8, 10, 10, 10, 10, 11, 12, 12. Again, the min median will be 10. Sufficient.
Statement 2 : y = 13
Arranging the elements in ascending order we get, x, x, x, x, 10, 10, 10, 10, 11, 12, 12, 13.
If x<= 10, the list will be as above and then the minimum median is 10, but if x >=13, then the list will be 10, 10, 10, 10, 11, 12, 12, 13, x, x, x, x. In this case the max median will be 12. So the median here can be any value from 10 to 12. Insufficient.
Hope this helps! Aditya



ISB School Moderator
Joined: 08 Dec 2013
Posts: 432
Location: India
Concentration: Nonprofit, Sustainability
WE: Operations (NonProfit and Government)

The twelve numbers shown represent, the ages, in years, of the twelve
[#permalink]
Show Tags
22 May 2019, 03:01
AdityaCrackVerbal wrote: This a perfect question that we can use the concept of maximization and minimization. There are three things to keep in mind while solving questions related to the median :
1. By definition, the median is the middle value in a list of numbers arranged in ascending or descending order. 2. The arrangement is always key to solving questions related to the median. 3. On questions where we have a list of elements with many variables, maximization and minimization is the best way to proceed.
Now lets jump into the solving of the question.
We have the list x, x, x, x, 8, 8, 8, 8, 12, 12, 11,y. Since the data here are of ages, x and y have to be integers.
Statement 1 : x = 10
Arranging the elements in ascending order we get, 8, 8, 8, 8, 10, 10, 10, 10, 11, 12, 12, y.
Now let us think about the max and min values of y. If y >= 12, then the max median will be 10. If y <= 12, then the list now becomes y, 8, 8, 8, 8, 10, 10, 10, 10, 11, 12, 12. Again, the min median will be 10. Sufficient.
Statement 2 : y = 13
Arranging the elements in ascending order we get, x, x, x, x, 10, 10, 10, 10, 11, 12, 12, 13.
If x<= 10, the list will be as above and then the minimum median is 10, but if x >=13, then the list will be 10, 10, 10, 10, 11, 12, 12, 13, x, x, x, x. In this case the max median will be 12. So the median here can be any value from 10 to 12. Insufficient.
Hope this helps! Aditya Hello Aditya, nice to see you on the gmatclub & thank you for the precise explanation. AdityaCrackVerbal
_________________
Kindly drop a '+1 Kudos' if you find this post helpful.GMAT Math Book I never wanted what I gave up I never gave up what I wanted




The twelve numbers shown represent, the ages, in years, of the twelve
[#permalink]
22 May 2019, 03:01






