Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
Re: In a certain set of five numbers the median is 200
[#permalink]
Show Tags
03 Mar 2012, 13:56
4
9
In a certain set of five numbers the median is 200. Is the range greater than 80?
Say the set is {a, b, 200, c, d}. Question: is d-a>80?
(1) The average (arithmetic mean) of the numbers is 240 --> the sum of the numbers is 240*5=1,200. Now, let's see whether the range can be less than 80, so let's try to minimize the range. The range will be minimized if we maximize a and minimize d. Maximum value of a as well as b is 200 and minimum value of d is c, so our set will be: {200, 200, 200, d, d} --> 600+2d=1,200 --> d=300 --> the range=d-c=300-200=100>80. Sufficient.
(2) Three of the numbers in the set are equal. Clearly insufficient.
Re: In a certain set of five numbers the median is 200
[#permalink]
Show Tags
14 May 2013, 18:00
1
Bunuel wrote:
In a certain set of five numbers the median is 200. Is the range greater than 80?
Say the set is {a, b, 200, c, d}. Question: is d-a>80?
(1) The average (arithmetic mean) of the numbers is 240 --> the sum of the numbers is 240*5=1,200. Now, let's see whether the range can be less than 80, so let's try to minimize the range. The range will be minimized if we maximize a and minimize d. Maximum value of a as well as b is 200 and minimum value of d is c, so our set will be: {200, 200, 200, d, d} --> 600+2d=1,200 --> d=300 --> the range=d-c=300-200=100>80. Sufficient.
(2) Three of the numbers in the set are equal. Clearly insufficient.
Re: In a certain set of five numbers the median is 200
[#permalink]
Show Tags
14 May 2013, 18:32
1
TheNona wrote:
Bunuel wrote:
In a certain set of five numbers the median is 200. Is the range greater than 80?
Say the set is {a, b, 200, c, d}. Question: is d-a>80?
(1) The average (arithmetic mean) of the numbers is 240 --> the sum of the numbers is 240*5=1,200. Now, let's see whether the range can be less than 80, so let's try to minimize the range. The range will be minimized if we maximize a and minimize d. Maximum value of a as well as b is 200 and minimum value of d is c, so our set will be: {200, 200, 200, d, d} --> 600+2d=1,200 --> d=300 --> the range=d-c=300-200=100>80. Sufficient.
(2) Three of the numbers in the set are equal. Clearly insufficient.
Answer: A.
why b is clearly insufficient ?
Lets say the set is a,b,200,c,d as taken by bunuel...
Now we donot know anything about the mean of the numbers.
If the numbers are 200,200,200,220,230 the range will be 30 If the numbers are 200,200,200,220,290 the range will be 40. and so onnnnnn....
So we cannot say desicively what the range is? Whether it is greater than 80 or not..So it is not sufficient
_________________
"Kudos" will help me a lot!!!!!!Please donate some!!!
Completed Official Quant Review OG - Quant
In Progress Official Verbal Review OG 13th ed MGMAT IR AWA Structure
Yet to do 100 700+ SC questions MR Verbal MR Quant
Re: In a certain set of five numbers the median is 200
[#permalink]
Show Tags
Updated on: 15 May 2013, 12:08
tom09b wrote:
In a certain set of five numbers the median is 200. Is the range greater than 80?
(1) The average (arithmetic mean) of the numbers is 240 (2) Three of the numbers in the set are equal
From F.S 1, as the average is 240, we can assume that each of the 5 elements is 240 . However , as the median is 200, the two elements below the median can be at-most 200 each and the two elements above median can be at-least 200 each. Now,Range = Max(element)-Min(element). After maximizing the 2 elements below the median, we can have the following set : 200,200,200,300,300. Now,to have a value of range=80, we would have to have the value of the Max(element) = 280. Notice : 200,200,200,320,280 --> The Max(element) changes to 320 . Thus, any change on the Max(element) will ALWAYS lead to a range>80.Also, any decrease on the Min(element) will only increase the numerical value of Range above 80. Sufficient.
From F.S 2, we can have either 160,180,200,200,200 where range<80 OR 100,120,200,200,200 where range>80. Insufficient.
Re: In a certain set of five numbers the median is 200
[#permalink]
Show Tags
15 May 2013, 00:46
2
TheNona wrote:
Bunuel wrote:
In a certain set of five numbers the median is 200. Is the range greater than 80?
Say the set is {a, b, 200, c, d}. Question: is d-a>80?
(1) The average (arithmetic mean) of the numbers is 240 --> the sum of the numbers is 240*5=1,200. Now, let's see whether the range can be less than 80, so let's try to minimize the range. The range will be minimized if we maximize a and minimize d. Maximum value of a as well as b is 200 and minimum value of d is c, so our set will be: {200, 200, 200, d, d} --> 600+2d=1,200 --> d=300 --> the range=d-c=300-200=100>80. Sufficient.
(2) Three of the numbers in the set are equal. Clearly insufficient.
Answer: A.
why b is clearly insufficient ?
Because it's easy to construct the sets which give two different answers to the question: {200, 200, 200, 201, 100000000} {200, 200, 200, 201, 202}
_________________
Re: In a certain set of five numbers the median is 200
[#permalink]
Show Tags
15 Dec 2016, 15:58
This is a great Question. Excellent Solutions have been provided above. Here is my solution to this one=>
Let the 5 numbers be in increasing order as =>
a b c d e
Now #=5
Hence median = 3rd term => c So c= 200
Now we are asked if range is >80 or not. Here we will calculate the minimum value of range and if the minimum value of range >80 then range will be great than 80
Statement 1=> Mean =240
There is a very important property of mean => Sum of deviations around the mean is always zero.
Now to minimise the range => a=b=c=200
Total negative deviation occurred =120 Hence to balance out this => d and e must have a 120 positive devotion when added. To minimise range we must minimise e for that we she maximise d d=e=300
Hence minimum range = 300-200=100
Hence sufficient
Statement 2--> Three values are equal Notice no mean is provided. E.g=> a=e=200=> Range =0 a=200 and e=999999 => Range>80 Hence insufficient
Re: In a certain set of five numbers the median is 200
[#permalink]
Show Tags
16 Dec 2016, 21:12
Bunuel wrote:
In a certain set of five numbers the median is 200. Is the range greater than 80?
Say the set is {a, b, 200, c, d}. Question: is d-a>80?
(1) The average (arithmetic mean) of the numbers is 240 --> the sum of the numbers is 240*5=1,200. Now, let's see whether the range can be less than 80, so let's try to minimize the range. The range will be minimized if we maximizea and minimize d. Maximum value of a as well as b is 200 and minimum value of d is c, so our set will be: {200, 200, 200, d, d} --> 600+2d=1,200 --> d=300 --> the range=d-c=300-200=100>80. Sufficient.
(2) Three of the numbers in the set are equal. Clearly insufficient.
In a certain set of five numbers the median is 200
[#permalink]
Show Tags
16 Dec 2016, 21:29
1
OreoShake wrote:
Bunuel wrote:
In a certain set of five numbers the median is 200. Is the range greater than 80?
Say the set is {a, b, 200, c, d}. Question: is d-a>80?
(1) The average (arithmetic mean) of the numbers is 240 --> the sum of the numbers is 240*5=1,200. Now, let's see whether the range can be less than 80, so let's try to minimize the range. The range will be minimized if we maximizea and minimize d. Maximum value of a as well as b is 200 and minimum value of d is c, so our set will be: {200, 200, 200, d, d} --> 600+2d=1,200 --> d=300 --> the range=d-c=300-200=100>80. Sufficient.
(2) Three of the numbers in the set are equal. Clearly insufficient.
Answer: A.
Bunuel, shouldnt it be minimize A and maximize D?
Hi You see, if we minimise a and maximise d => The range would be maximum. we have to check for the minimum value of range. E.g=> Lets see an example with 3 numbers => a,b,c Median = 100 => b=100 a,100,c be the three numbers in increasing order. a=0 c=200 the range = 200
if a=100 c=100 Range =0
Hence we have to maximise a and minimise d in our original question
Re: In a certain set of five numbers the median is 200
[#permalink]
Show Tags
05 Jan 2018, 05:27
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.
_________________
close
45% (02:17) correct 
