A number theory problem by A Former Brilliant Member

Number Theory Level 2

How many two digit numbers exist such that when the product of its digits is added to the sum of its digit , the result we get is the original two digit number.


The answer is 9.

A Former Brilliant Member by A Former Brilliant Member

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3 solutions

Anand Raj
Aug 17, 2014

solving: x + y + xy = 10x + y; we get y=9: x can be any positive integer...... So numbers are:

19

29

39

49

59

69

79

89

99

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Ivan Martinez
Sep 28, 2014

-Let the 2 digit number be: 10x+y. -Then 10xy+x+y=20x+y. -Solving the equation we get: y= 9. -Therefore all the two digit number ending in 9 has the mentioned propery.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

xy+x+y=10x+y.......solving it we get y=9.... since we get nine two digit numbers with last digit as 9,therefore,the answer is 9 nos

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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