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Set X consists of 11 different numbers. If the average (arithmetic mea
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03 Aug 2022, 09:19
03 Aug 2022, 09:19
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Set X consists of 11 different numbers. If the average (arithmetic mean) of the 10 smallest numbers is -1.6, and the average of the 10 largest numbers is 5.2. What is the range of set X?
A. 3.6
B. 6.8
C. 34
D. 36
E. 68
A. 3.6
B. 6.8
C. 34
D. 36
E. 68
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Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
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WE:Engineering (Computer Software)
Re: Set X consists of 11 different numbers. If the average (arithmetic mea
[#permalink]
04 Aug 2022, 23:08
04 Aug 2022, 23:08
Theory
Set X consists of 11 different numbers
Let the Sum of these 11 numbers be S
The average (arithmetic mean) of the 10 smallest numbers is -1.6
Sum of 10 smallest numbers = Average * 10 = -1.6*10 = -16
Sum of 11 numbers = Sum of 10 smallest numbers + Largest Number
=> S = -16 + Largest Number
=> Largest Number = S + 16
The average of the 10 largest numbers is 5.2
Sum of 10 largest numbers = Average * 10 = 5.2*10 = 52
Sum of 11 numbers = Smallest number + Sum of 10 largest numbers
=> S = Smallest Number + 52
=> Smallest Number = S - 52
Range = Largest Number - Smallest Number = S + 16 - (S-52) = S-S + 16 + 52 = 68
So, Answer will be E.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
- ➡ Average = Sum of all the Values / Total Number of Values
➡ Sum of All the values = Average * Total Number of Values
➡ Range = Highest Value - Lowest Value = Largest Value - Smallest Value
Set X consists of 11 different numbers
Let the Sum of these 11 numbers be S
The average (arithmetic mean) of the 10 smallest numbers is -1.6
Sum of 10 smallest numbers = Average * 10 = -1.6*10 = -16
Sum of 11 numbers = Sum of 10 smallest numbers + Largest Number
=> S = -16 + Largest Number
=> Largest Number = S + 16
The average of the 10 largest numbers is 5.2
Sum of 10 largest numbers = Average * 10 = 5.2*10 = 52
Sum of 11 numbers = Smallest number + Sum of 10 largest numbers
=> S = Smallest Number + 52
=> Smallest Number = S - 52
Range = Largest Number - Smallest Number = S + 16 - (S-52) = S-S + 16 + 52 = 68
So, Answer will be E.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
gmatclubot
Re: Set X consists of 11 different numbers. If the average (arithmetic mea [#permalink]
04 Aug 2022, 23:08
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