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January 4th, 2012, 06:09 PM   #1
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Finding two digit number

Can anyone help me with this problem?
Five two-digit numbers are multiples of the products of their digits. Four of these numbers are 11, 12, 24, and 36. Find the fifth number.
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January 4th, 2012, 06:41 PM   #2
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Re: Finding two digit number

If a = 1 and b = 5, k is an integer; answer: 15.
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January 4th, 2012, 07:44 PM   #3
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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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