Xavier Aptitude Test 2013 Paper

Question : 72 of 121

Marks: +1, -0

A number is interesting if on adding the sum of the digits of the number and the product of the digits of the number, the result is equal to the number. What fraction of numbers between 10 and 100 (both 10 and 100 included) is interesting?

0.1
0.11
0.16
0.22
None of the above

Validate

Solution:

(a) Let the numbers be the form 10x + y
According to question
10x + y = x + y + xy
9x = xy
∴ y = 9
The numbers are 19, 29, 39, 49, 59, 69, 79, 89 and 99 –
total of 9 numbers
Hence the required fraction =

9/91

= 0.099 ≈ 0.1

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