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The average (arithmetic mean) of a list of 8 different positive.......
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07 Feb 2019, 09:30
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The average (arithmetic mean) of a list of 8 different positive integers is 23. Which of the following is the greatest possible range of this list of numbers? A) 149 B) 155 C) 156 D) 168 E) 183
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Re: The average (arithmetic mean) of a list of 8 different positive.......
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07 Feb 2019, 10:47
CAMANISHPARMAR wrote: The average (arithmetic mean) of a list of 8 different positive integers is 23. Which of the following is the greatest possible range of this list of numbers?
A) 149 B) 155 C) 156 D) 168 E) 183 Since we need a list 8 +ve integers and their mean is 23, then their sum is 23*8 = 184 Now lets us try to minimize the first 7 and maximize the 8th number. First 7 numbers will be = 1, 2, 3, 4, 5, 6, 7 whose sum = 28 And hence the 8th number will be 18428 = 156 Now the range is = 156 1 = 155 Hence B is the correct answer.
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The average (arithmetic mean) of a list of 8 different positive.......
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Updated on: 07 Feb 2019, 11:09
Sum of all the numbers = Mean *total numbers =23*8=184
Now max range will happen when we have maxmin of a set.
Lets assume max =184 Now rest 7 digits need to be different and positive so .. 1,2,3,4,5,6,7
Therefore,largest term is
184(1+2+3+4+5+6+7)
184 (sum of AP till 7 or you can simply add )
184 7*8/2
18428
=156
Therefore range is Largest termSmallest term =1561 =155
Hope it helps !!
Posted from my mobile device
Originally posted by prabsahi on 07 Feb 2019, 11:01.
Last edited by prabsahi on 07 Feb 2019, 11:09, edited 1 time in total.



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Re: The average (arithmetic mean) of a list of 8 different positive.......
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07 Feb 2019, 11:03
CAMANISHPARMAR wrote: The average (arithmetic mean) of a list of 8 different positive integers is 23. Which of the following is the greatest possible range of this list of numbers?
A) 149 B) 155 C) 156 D) 168 E) 183 keyword : 8 different positive integers Now Range = Highest Term  Lowest term Average = 23, Total sum = 184 (23*8) Now if i minimize Lowest term, i can maximize Highest Term 1 2 3 4 5 6 7 156 1561 = 155 B
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Re: The average (arithmetic mean) of a list of 8 different positive.......
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10 Feb 2019, 20:39
CAMANISHPARMAR wrote: The average (arithmetic mean) of a list of 8 different positive integers is 23. Which of the following is the greatest possible range of this list of numbers?
A) 149 B) 155 C) 156 D) 168 E) 183 The sum of the integers is 8 x 23 = 184. To maximize the range, we need the largest element to be as large as possible and the smallest element to be as small as possible. To find the largest possible value in the set, we should take the rest of the elements as small as possible. Thus, we can let the first 7 integers be 1, 2, 3, 4, 5, 6, 7, for a sum of 28, so the largest value in the set would be 184  28 = 156, for a maximum range of 156  1 = 155. Answer: B
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The average (arithmetic mean) of a list of 8 different positive.......
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11 Feb 2019, 08:16
Can someone please explain why we need to subtract 1 from 156?
How do we know when we need to subtract from 1 and when not to when working with ranges?
Thank you in advance!



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Re: The average (arithmetic mean) of a list of 8 different positive.......
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11 Feb 2019, 08:24
jojo95 wrote: Can someone please explain why we need to subtract 1 from 156?
How do we know when we need to subtract from 1 and when not to when working with ranges?
Thank you in advance! Hey jojo95Range is calculated in terms of Highest Term  Lowest Term in a arithmetic series, or an evenly spaced series. We use the mentioned formula. And since the question is pertaining to that concept we had to use that. Now i believe, you are talking about, how to calculate numbers from 5 to 10 In this case we use m  n  1, here you are subtracting 1. Next case will be how to calculate numbers between 5 and 10 In this case we use m  n + 1, here you are adding 1, to get the numbers between that range.
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The average (arithmetic mean) of a list of 8 different positive.......
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11 Feb 2019, 08:48
jojo95 wrote: Can someone please explain why we need to subtract 1 from 156?
How do we know when we need to subtract from 1 and when not to when working with ranges?
Thank you in advance! Range = Largest number  Smallest number Largest number = 156 Smallest number = 1 What will be the Range? Off course 156  1 = 155 This is not a special case. In fact, there is never ever a special case when dealing with the range formula. It is always the Largest number  Smallest number. It is just a coincidence that the smallest number is 1; that's why we are subtracting 1.
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