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The sum of a sequence of consecutive integers is 1,125 and t
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02 Apr 2020, 08:06
02 Apr 2020, 08:06
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The sum of a sequence of consecutive integers is 1,125 and the median is 45. What is the value of the greatest integer in the sequence?
A. 33
B. 45
C. 56
D. 57
E. 58
Kudos for the right answer and explanation
A. 33
B. 45
C. 56
D. 57
E. 58
Kudos for the right answer and explanation
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: The sum of a sequence of consecutive integers is 1,125 and t
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02 Apr 2020, 09:19
02 Apr 2020, 09:19
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Carcass wrote:
The sum of a sequence of consecutive integers is 1,125 and the median is 45. What is the value of the greatest integer in the sequence?
A. 33
B. 45
C. 56
D. 57
E. 58
Kudos for the right answer and explanation
A. 33
B. 45
C. 56
D. 57
E. 58
Kudos for the right answer and explanation
We are told that the median is 45
In other words, when all of the consecutive numbers are arranged in ascending order, 45 is the middlemost number.
Now let's add a number on either side of 45 to get: 44, 45, 46
This is the same as writing: (45-1), 45, (45+1), and if we add these three values, the -1 and +1 cancel out to get: 45 + 45 + 45
The same applies to when we add TWO numbers on either side of 45
We get: (45-2), (45-1), 45, (45+1), (45+2)
If we add these five values, the -1 and +1 cancel out, and the -2 and +2 cancel out to get : 45 + 45 + 45 + 45 + 45
1,125/45 = 25
So our sequence must consist of 25 values.
12 values must be greater than 45
12 values must be less than 45
And 1 value is equal to 45
So our sequence looks like this: (45-12), (45-11), (45-10), ..... (45-2), (45-1), 45, (45+1), (45+2)...., (45+10), (45+11), (45+12)
What is the value of the greatest integer in the sequence?
The greatest possible value = (45+12), which equals 57
Answer: D
Cheers,
Brent
Re: The sum of a sequence of consecutive integers is 1,125 and t
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17 Apr 2024, 15:56
17 Apr 2024, 15:56
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