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January 4th, 2012, 06:09 PM  #1 
Newbie Joined: Jan 2012 Posts: 28 Thanks: 0  Finding two digit number
Can anyone help me with this problem? Five twodigit numbers are multiples of the products of their digits. Four of these numbers are 11, 12, 24, and 36. Find the fifth number. 
January 4th, 2012, 06:41 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,929 Thanks: 1124 Math Focus: Elementary mathematics and beyond  Re: Finding two digit number If a = 1 and b = 5, k is an integer; answer: 15. 
January 4th, 2012, 07:44 PM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Finding two digit number
Let x be the first digit (tens place) and y be the second digit (ones place). Since it is stated that there are only 5 such numbers, then we must exclude y = 0. We then require: where and We see that y may be 1, 2 or 5 when x = 1, so We see that y may be 4 when x = 2, so We see that y may be 6 when x = 3, so Examination of the remaining values of x produce no other numbers satisfying the given conditions. 

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