What is the average of the consecutive integers m through n, inclusiv

Question

What is the average of the consecutive integers m through n, inclusive?

(1) The average of m and n is 23.5

(2) The average of the integers between m and n not including either is 23.5

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Conquistador23 · Answer

I think both options together are not enough to answer the question.

sanjitscorps18 · Answer

1. Say for eg. the numbers are 23 as m and 24 as n. Other pairs that have an average of 23.5 can be 22 & 25, 0 and 47, etc. If we count the consecutive integers between any of these pairs we would get the same average as 23.5. The sequence would always have an even count of numbers --> Sufficient

2. The average of the integers between m and n not including either is 23.5
This is an extension of statement 1. Say for eg the consecutive numbers 22, 23, 24, and 25 are between 21(m) and 26(n). Since the series and the extensions on both 21(m) and 26(n) have the same average, the overall series would have an average of 23.5. --> Sufficient

Option D

JeffTargetTestPrep · Answer

We need to find the average of consecutive integers whose lowest item is m and whose highest item is n, or vice versa.

We should see that consecutive integers are consecutive terms in an arithmetic sequence. For any arithmetic sequence, the average of terms can be determined with the following formula:

Average = (Lowest value + Highest value)/2

So, the question is:

(m + n)/2 = ?

Statement One Alone:

=> The average of m and n is 23.5

(m + n)/2 = 23.5

Statement one is sufficient. Eliminate answer choices B, C, and E.

Statement Two Alone:

=> The average of the integers between m and n not including either is 23.5

We see that the integers between m and n are consecutive terms in an arithmetic sequence.

So, if m is less than n, the average of terms for this shorter sequence is:

/2 = 23.5

(m + n)/2 = 23.5

Statement two is sufficient.

Answer: D

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What is the average of the consecutive integers m through n, inclusiv

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What is the average of the consecutive integers m through n, inclusiv

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