BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Partial information on averages

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Tue Oct 09, 2012 4:46 am

Partial information on averages

by pradeepfriend2000 » Wed Apr 17, 2013 11:42 pm
Hi,

I encountered below probelm in manhattan tests. Can anybody give me easy explanation?
-----
List R contains five numbers that have an average value of 55. If the median of the numbers in the list is equal to the mean, and the largest number is equal to 20 more than three times the smallest number, what is the largest possible range for the numbers in the list?


a) 78
b) 77 1/5
c) 66 1/7
d) 55 1/7
e) 52

Correct answer is: A
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 511
Joined: Wed Aug 11, 2010 9:47 am
Location: Delhi, India
Thanked: 344 times
Followed by:86 members

by Anju@Gurome » Thu Apr 18, 2013 12:35 am
pradeepfriend2000 wrote:List R contains five numbers that have an average value of 55. If the median of the numbers in the list is equal to the mean, and the largest number is equal to 20 more than three times the smallest number, what is the largest possible range for the numbers in the list?
Say the numbers are a, b, c, d, and e; where a ≤ b ≤ c ≤ d ≤ e
Now, median = c = 55
and, e = (3a + 20)

Therefore, range = (max - min) = (e - a) = (2a + 20)
Therefore to maximize the range we have to maximize a.

Also, (a + b + c + d + e) = 5*55 = 275
--> (a + b + 55 + d + 3a + 20) = 275
--> (4a + b + d) = 200
--> 4a = (200 - b - d)

Now, a will be maximum when both b and d will be minimum.
Minimum value of b is a and that of d is c, i.e. 55.

Hence, when a is minimum,
  • 4a = (200 - a - 55) --> 5a = 145 --> a = 29
Hence maximum value of the range is (2*29 + 20) = 78

The correct answer is A.
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Top
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Tue Oct 09, 2012 4:46 am

by pradeepfriend2000 » Thu Apr 18, 2013 1:41 am
Thank you very much. Now I realised where I went wrong .
Top
Post new topic Post Reply
• Page 1 of 1