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21 Mar 2022, 06:45
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C
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Difficulty:
55%
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Question Stats:
71% (03:01) correct
29%
(02:59)
wrong
based on 238
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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
Are You Up For the Challenge: 700 Level Questions
A. 5
B. 7
C. 8
D. 9
E. 10
Are You Up For the Challenge: 700 Level Questions
21 Mar 2022, 07:07
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Given: 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.
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?
Let the six consecutive positive integers be
a-2,a-1,a,a+1,a+2,a+3
The sum of a sequence of six consecutive positive integers is Z
6a + 3 = Z
The sum of terms in a different sequence of five consecutive integers is Z − 5.
Let the sequence be
b-2,b-1,b,b+1,b+2
The sum of terms in a different sequence of five consecutive integers = 5b = Z − 5
Z = 5b + 5 = 6a + 3
The greatest term of the five-number sequence is 40
b+2 = 40; b = 38
Z = 5b + 5 = 195 = 6a + 3
a = 32
The difference between the median term of the five-number sequence and the least term of the six-number sequence = |b-(a-2)| = |38 - 30| = 8
IMO C
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?
Let the six consecutive positive integers be
a-2,a-1,a,a+1,a+2,a+3
The sum of a sequence of six consecutive positive integers is Z
6a + 3 = Z
The sum of terms in a different sequence of five consecutive integers is Z − 5.
Let the sequence be
b-2,b-1,b,b+1,b+2
The sum of terms in a different sequence of five consecutive integers = 5b = Z − 5
Z = 5b + 5 = 6a + 3
The greatest term of the five-number sequence is 40
b+2 = 40; b = 38
Z = 5b + 5 = 195 = 6a + 3
a = 32
The difference between the median term of the five-number sequence and the least term of the six-number sequence = |b-(a-2)| = |38 - 30| = 8
IMO C
22 Mar 2022, 23:14
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Sum of 6 Consecutive = 6n+15 (First term is n, Second is n+1 ...) = Z
Sum of 5 Consecutive with 40 as the greatest = 5(40+36)/2 = 190 = Z-5
190= 6N+15-5
N=30
Median of (36,37,38,39,40) = 38
Hence,
Median - Least of 6 consecutive
= 38-30
=8
Sum of 5 Consecutive with 40 as the greatest = 5(40+36)/2 = 190 = Z-5
190= 6N+15-5
N=30
Median of (36,37,38,39,40) = 38
Hence,
Median - Least of 6 consecutive
= 38-30
=8
