Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 10 Jan 2010
Posts: 89
GPA: 4
WE: Programming (Computer Software)

At a delivery store, seven packages have an average (arithme
[#permalink]
Show Tags
20 Sep 2011, 20:17
Question Stats:
70% (02:22) correct 30% (02:19) wrong based on 513 sessions
HideShow timer Statistics
At a delivery store, seven packages have an average (arithmetic mean) weight of 225 pounds and a median weight of 270 pounds. What is the maximum possible weight, in pounds, of the lightest package? A. 25 B. 165 C. 195 D. 225 E. 270
Official Answer and Stats are available only to registered users. Register/ Login.




Manager
Joined: 14 Mar 2011
Posts: 183

Re: Mean, Median
[#permalink]
Show Tags
20 Sep 2011, 20:43
Total weight of 7 packages = 225 * 7 = 1575 pounds.
In a set of 7 numbers, 4th element will be the middle one and hence median. weight of 4th element =270 pounds. to maximise weight of lightest package, minimize the weight of others. 4th number is 270, so let the 5th 6th and 7th number of the set also be 270 pounds which is least possible weight they can have. total weight of 4th, 5th , 6th and 7th numbers = 270 *4 = 1080 pounds.
so total weight remaining to be shared by 1st 2nd and 3rd number = 1575  1080= 495 pounds. let the 1st 2nd and 3rd element have the same value. so they can be 495/3 = 165 pounds each. so lightest package is 165 pounds in weight.




Manager
Status: Bell the GMAT!!!
Affiliations: Aidha
Joined: 16 Aug 2011
Posts: 127
Location: Singapore
Concentration: Finance, General Management
GMAT 1: 680 Q46 V37 GMAT 2: 620 Q49 V27 GMAT 3: 700 Q49 V36
WE: Other (Other)

Re: Mean, Median
[#permalink]
Show Tags
21 Sep 2011, 01:52
maheshsrini wrote: At a delivery store, seven packages have an average (arithmetic mean) weight of 225 pounds and a median weight of 270 pounds. What is the maximum possible weight, in pounds, of the lightest package?
a) 25 b)165 c)195 d)225 e)270 IMO B. You can eliminate options D and E with intuition. For average to be 225 and median to be 270, the lightest item has to be less than 225. If not, the average will be more than 225. Hence D and E are eliminated. Now since, option C looks closer to 225, test option B (165) first. I dint even test this case to come to answer. (I guess this is how you visualise the question).



Manager
Joined: 30 Sep 2009
Posts: 80

Re: Mean, Median
[#permalink]
Show Tags
21 Sep 2011, 04:10
for this type of question:
we know that median is 270 that means the 4th element in the set is 270. for maximum smallest integer we have to assume that the 5,6,7 will also be 270 and that smallest 3 element must be same.
hence, 3*x+270*4=225*7 hence x=165.



Intern
Status: Need to read faster and get less distracted by the ticking clock!
Affiliations: Golden Key
Joined: 19 Nov 2010
Posts: 12
Location: Toronto, ON
Schools: INSEAD, ISB, NUS

Re: Mean, Median
[#permalink]
Show Tags
21 Sep 2011, 11:47
B.
225x 7 = 1575 total.
Lets say all options on right of 270 is 270.. therefore remaining three have to have total weight of: 1575  (270x4) = 495 495/3 = 165!



Manager
Joined: 10 Jan 2011
Posts: 112
Location: India
GMAT Date: 07162012
GPA: 3.4
WE: Consulting (Consulting)

Re: Mean, Median
[#permalink]
Show Tags
27 Sep 2011, 10:58
225*7 = 3X + 270*4 15751080 = 3X 495/3 = X X= 165
_________________
Analyze why option A in SC wrong



Intern
Joined: 05 Jul 2011
Posts: 10

Re: Mean, Median
[#permalink]
Show Tags
28 Sep 2011, 08:06
I got B too.. Assuming all options on right of
270 is 270, then we get 3x + 270*4 = 225*7 3x = 15751080 x = 495/3 x= 165



Current Student
Joined: 21 Aug 2010
Posts: 176

Re: Mean, Median
[#permalink]
Show Tags
28 Sep 2011, 12:08
It is B. But I don't understand how come it's 700 level question.
BR Mandeep



Intern
Joined: 04 Oct 2011
Posts: 8

Re: Mean, Median
[#permalink]
Show Tags
05 Oct 2011, 10:42
Total number 7
mean 225 median 270 = 4th number = 270 to get a biggest first number the other numbers should be minimum = 4th , 5 th , 6 th and 7 th numbers are equal to median
= 45 more than mean that add ups 180
180 more than mean
the sum of first three numbers = 3*225  180 = 495
biggest first number = 165



Intern
Joined: 18 Feb 2013
Posts: 1

Re: At a delivery store, seven packages have an average (arithme
[#permalink]
Show Tags
22 Oct 2013, 08:26
Yes, but they do not have to be the same number, The smallest elements have to be smaller than the median and sum 495. So it would be correct to pick 195,200 and 200. can somebody explain why the smallest number has to be the same?? The question asks about maximum value of the smallest not of the three smallests...



Intern
Joined: 11 Jul 2013
Posts: 31

Re: At a delivery store, seven packages have an average (arithme
[#permalink]
Show Tags
07 May 2014, 00:56
Petepie wrote: Yes, but they do not have to be the same number, The smallest elements have to be smaller than the median and sum 495. So it would be correct to pick 195,200 and 200. can somebody explain why the smallest number has to be the same?? The question asks about maximum value of the smallest not of the three smallests... sum of first three is 495, in your case the sum (195+200+200) equals 595 . kindly recheck



Intern
Joined: 08 Jan 2014
Posts: 16
Location: United States
Concentration: General Management, Entrepreneurship
GMAT Date: 06302014
GPA: 3.99
WE: Analyst (Consulting)

Re: At a delivery store, seven packages have an average (arithme
[#permalink]
Show Tags
08 May 2014, 13:37
B. 7 packages. Median is 4th package. Weight of median is 270.
to maximise weight of lightest package, minimize the weight of others. so the 5th 6th and 7th number of the set also be 270 pounds which is least possible weight they can have. total weight of 4th, 5th , 6th and 7th numbers = 270 *4 = 1080 pounds.
so total weight remaining to be shared by 1st 2nd and 3rd number = 1575  1080= 495 pounds. let the 1st 2nd and 3rd element have the same value. so they can be 495/3 = 165 pounds each. so lightest package is 165 pounds in weight.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9869
Location: Pune, India

Re: At a delivery store, seven packages have an average (arithme
[#permalink]
Show Tags
08 May 2014, 22:46
maheshsrini wrote: At a delivery store, seven packages have an average (arithmetic mean) weight of 225 pounds and a median weight of 270 pounds. What is the maximum possible weight, in pounds, of the lightest package?
A. 25 B. 165 C. 195 D. 225 E. 270 For a discussion of MinMax strategies, check out the following posts: http://www.veritasprep.com/blog/2014/01 ... thegmat/http://www.veritasprep.com/blog/2014/01 ... basecase/http://www.veritasprep.com/blog/2014/01 ... extremes/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Math Expert
Joined: 02 Sep 2009
Posts: 59675

Re: At a delivery store, seven packages have an average (arithme
[#permalink]
Show Tags
09 May 2014, 02:14



Current Student
Joined: 12 Aug 2015
Posts: 2551

At a delivery store, seven packages have an average (arithme
[#permalink]
Show Tags
15 Dec 2016, 15:08
Great Question this one. Here is my approach to this one =>
Let the packages be represented by => W1 W2 W3 W4 W5 W6 W7
Mean = 225
Mean = Sum/#
Hence Sum(7)=225*7=1575 Now median =270 #=7=> Odd Hence Median = 4th term = W4=270
Now to Maximise W1 we must minimise all others.
W1=W2=W3=W1 W4=W5=W6=W7=270
Hence 3W1+4*270=1575 3W1=495 W1=165 Pounds
Hence B
_________________



NonHuman User
Joined: 09 Sep 2013
Posts: 13737

Re: At a delivery store, seven packages have an average (arithme
[#permalink]
Show Tags
01 Oct 2018, 12:09
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.
_________________




Re: At a delivery store, seven packages have an average (arithme
[#permalink]
01 Oct 2018, 12:09






