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21 Aug 2018, 06:01
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If the average (arithmetic mean) of 24 consecutive odd integers is 48, what is the median of the 24 numbers?
A. 36
B. 47
C. 48
D. 49
E. 72
A. 36
B. 47
C. 48
D. 49
E. 72
21 Aug 2018, 06:17
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Bunuel
If the average (arithmetic mean) of 24 consecutive odd integers is 48, what is the median of the 24 numbers?
A. 36
B. 47
C. 48
D. 49
E. 72
A. 36
B. 47
C. 48
D. 49
E. 72
As the number of elements are consecutive and is an Even number 24, hence the median should be equal to mean because the distribution is symmetric
Median will be the average of 12th & 13th term, which are odd numbers, hence their average will be an Even number.
Among the options only \(48\) is close to mean. Hence our answer
Option C
---------------------
Method 2: Using progression
\(Sum = \frac{n}{2}*[2a+(n-1)*d]\), here
\(Sum = 48*24\), \(n=24\), \(d=2\) we need \(a\)
\(=>48*24=\frac{24}{2}*(2a+23*2)\)
\(=>a=25\)
Now, \(T_{12}=a+(n-1)d=>a+11*2=25+22=47\)
therefore, \(T_{13}=47+2=49\)
Hence median \(= \frac{(47+49)}{2}=48\)
Option C
21 Aug 2018, 08:47
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Bunuel
If the average (arithmetic mean) of 24 consecutive odd integers is 48, what is the median of the 24 numbers?
A. 36
B. 47
C. 48
D. 49
E. 72
I. Rule: In ANY evenly spaced set of integers, the median equals the mean A. 36
B. 47
C. 48
D. 49
E. 72
Median = mean = 48
ANSWER C
II. Test a smaller but similar sample
Use an even number of terms. Four consecutive odd integers: {1, 3, 5, 7}
Median = "middle value." If the number of terms is even, median =
average of the two middle terms: \(\frac{(3+5)}{2}=4\)
Mean = \(\frac{(1+3+5+7)}{4}=4\)
So median = mean. In prompt, mean = 48
Median also = 48
ANSWER C
Further, in any evenly spaced set --
median AND mean = \(\frac{FirstTerm+ LastTerm}{2}\)
everything simple is unique 
