Bunuel wrote:
The sum of a sequence of six consecutive positive integers is Z. The sum of terms in a different sequence of five consecutive integers is Z − 5. If the greatest term of the five-number sequence is 40, what is the difference between the median term of the five-number sequence and the least term of the six-number sequence?
A. 5
B. 7
C. 8
D. 9
E. 10
Given:
1. The sum of a sequence of six consecutive positive integers is Z.
2. The sum of terms in a different sequence of five consecutive integers is Z − 5.
Asked: If the greatest term of the five-number sequence is 40, what is the difference between the median term of the five-number sequence and the least term of the six-number sequence?
1. The sum of a sequence of six consecutive positive integers is Z.
Let the sequence be {a, a+1, a+2, a+3, a+4, a+5}
a + a+1 + a+2 + a+3 + a+4 + a+5 = Z
6a + 15 = Z
2. The sum of terms in a different sequence of five consecutive integers is Z − 5.
b + b+ 1 + b+2 + b+3 + b+4 = Z -5 = 6a + 15 - 5 = 6a + 10
5b + 10 = 6a + 10
5b = 6a
3. The greatest term of the five-number sequence is 40.
b + 4 = 40
b = 36
5b = 6a
5*36 = 6a
a = 30
Median term of 5-number sequence = b + 2 = 38
Least term of 6-number sequence = a = 30
The difference between the median term of the five-number sequence and the least term of the six-number sequence = 38 - 30 = 8
IMO C
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com