What is the median of the set of all three digit natural numbers such that the units digit is greate...........

Quantitative Aptitude (CDS) Statistics

What is the median of the set of all three digit natural numbers such that the units digit is greater than the tens digit which is greater than the hundred’s digit?

263

258.5

345

278.5

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Explanation:

Let the three digit number be a b c. Hence, a Similarly, a=1, b=2, c=4-9 (6 numbers). Hence # of numbers starting with 1 = (7+6+5+4+3+2+1) =28.
Starting with 2 = (6+5+..+1) = 21. Hence, the number of numbers are = 28+21+15+10+6+3+1=84.
Hence median is average of 42nd and 43rd term. 28+21= 49 terms are less than 300.
Hence 289-49, 279-48, 278-47, 269-46, 268 – 45, 267-44, 259-43 and 258-42.
Hence 42nd term is 258 and 43rd is 259. Hence median is 258.5.