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K is a two digits number, if the sum of the tens' and units'

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Senior Manager
Joined: 14 Jul 2006
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K is a two digits number, if the sum of the tens' and units' [#permalink]  17 Aug 2006, 06:35
. K is a two digits number, if the sum of the tens' and units' digit is 3 less than the product of each digit. What is the value of K?

Hi guys any ideas on how to tackle this problem?
Senior Manager
Joined: 05 Mar 2006
Posts: 348
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x+y = xy - 3

xy - y = 3 + x

y(x-1) = (3+x)

y = (3+x)/(x-1)

If we plug in X = 1 through 9 we get intergers for Y for the following two digit numbers:

25
33
52
Senior Manager
Joined: 14 Jul 2006
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Thanks for the help
VP
Joined: 02 Jun 2006
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question needs to be refined..

If K = 10x+y, then
K = {25,52, 33}

BTW for any problem which refers to a two digit problem, use the K = 10x+y way of representing the digits .. Makes it easier..
Then again, you might already know that
Senior Manager
Joined: 14 Jul 2006
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Hi,

Thanks for the tip. But in this case how do you utilize the 10x+y thingie?
VP
Joined: 02 Jun 2006
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Yes, for this problem it doesn't help.. but in general there are problems which ask you to flip the digits and find the possible sums.

For ex. if the digits of a two digit number are flipped and the two numbers added, which of the following is a possible sum..
So K= 10x+y, K'=10y+x,
K+K' = 11(x+y)...
Sum has to be a multiple of 11,

Same way with difference .. K-K' = 9(x-y)
If (x+y) or (x-y) is given you can find the difference or sum.

Again, you might already know this.
apollo168 wrote:
Hi,

Thanks for the tip. But in this case how do you utilize the 10x+y thingie?
Senior Manager
Joined: 14 Jul 2006
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Ah yeah that's right. Ive encountered a few of those types of problems

THanks
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