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Five numbers in a set are arranged from least to greatest. If the median of the first two numbers is 13 and the average (arithmetic mean) of the remaining numbers is 23, what is the average (arithmetic mean) of the entire set?
A. 13
B. 19
C. 21
D. 22
E. 23
A. 13
B. 19
C. 21
D. 22
E. 23
17 Mar 2022, 08:51
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let numbers be a,b,c,d,e (increasing order)
so median of a,b = (a+b)/2 = 13
ie, a+b =26
average of c,d,e = 23
ie, (c+d+e)/3 = 23
ie, c+d+e = 69
therefore, a+b+c+d+e = 26+69 =95
average of a,b,c,d,e = 95/5 = 19
Ans B
so median of a,b = (a+b)/2 = 13
ie, a+b =26
average of c,d,e = 23
ie, (c+d+e)/3 = 23
ie, c+d+e = 69
therefore, a+b+c+d+e = 26+69 =95
average of a,b,c,d,e = 95/5 = 19
Ans B
17 Mar 2022, 08:58
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The median of two numbers is the average of the two numbers, so we really just have a standard weighted average situation: we're combining one set with an average of 13 with another set with an average of 23. The sizes of the sets are in a 2 to 3 ratio. Now any weighted average method will solve the problem -- using alligation, for example, you can see the answer is 19 almost immediately.
