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Two Digit Average (Posted on 2007-05-04) Difficulty: 1 of 5
There is a two digit number with the unique property that if a decimal point is inserted between the two digits, the resulting number is the average of the digits. What is the number?

See The Solution Submitted by Brian Smith    
Rating: 3.2500 (4 votes)

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Solution An Alternate Methodology | Comment 3 of 4 |
Let the two digit number be written as ab in the decimal system. Hence, a must be non zero. 

By the problem:
a.b = Average (a, b)
Or, (a.b) = (a+b)/2 ................(#)

Since a+b is a whole number, it follows in terms of (#) that:
b is either 0 or 5.

If b is 0, then:

a.0 = a/2, giving:
a =0;  which is a contradiction as a must  be non zero.

Thus b=5, giving:
2*(a.5) = a+ 5
Or, 2a+1 = a+5
Or, a = 4

Thus, our desired two digit number is 45. 

Edited on May 4, 2007, 11:31 am
  Posted by K Sengupta on 2007-05-04 11:26:06

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