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K is a two-digit number, if the sum of the tens and unit

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K is a two-digit number, if the sum of the tens and unit [#permalink] New post 05 Apr 2006, 08:53
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K is a two-digit number, if the sum of the tens and unit digits is 3 less than the product of the two digits. What is the value of K?
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 [#permalink] New post 05 Apr 2006, 09:12
K is a two-digit number, if the sum of the tens and unit digits is 3 less than the product of the two digits. What is the value of K?

Let's set the tens digit as x and the units digit as y.

X+Y+3 = X*Y

I think that this then requires a slight bit of logic. X and Y need to be small because otherwise their product would be too great. After considering a couple of values, I can say that K is 33.

Is their a "foolproof" method to solving that equation? I realized that the equation could be set as x - xy + y = -3, but couldn't remember how to solve for x and y as a quadratic. Any thoughts?
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 [#permalink] New post 05 Apr 2006, 09:34
K = 10A + B
A + B = A*B-3
A*B - A = B + 3
A*(B - 1) = B + 3
A = (B + 3)/(B - 1)

Then check the possible cases where both A and B
are integers. Start with B = 0 and end with B = 9.

This leads to 52, 33 and 25, so K cannot be determined.
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 [#permalink] New post 05 Apr 2006, 10:22
I agree...k cannot be determined without further information.
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Re: PS find k [#permalink] New post 05 Apr 2006, 12:27
yah, there are more than one solution, Laxi.

laxieqv wrote:
K is a two-digit number, if the sum of the tens and unit digits is 3 less than the product of the two digits. What is the value of K?


how about -30 [10(-3) + 0], since 3 is -ve and 0 cannot be -ve or +ve.

sum = -3
product = 0
diff = -3

though it is only an additional one but i am not sure how correct it is?
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 [#permalink] New post 06 Apr 2006, 13:52
when K has several values,
given in the choice one can select the right answer.



ccax wrote:
K = 10A + B
A + B = A*B-3
A*B - A = B + 3
A*(B - 1) = B + 3
A = (B + 3)/(B - 1)

Then check the possible cases where both A and B
are integers. Start with B = 0 and end with B = 9.

This leads to 52, 33 and 25, so K cannot be determined.
  [#permalink] 06 Apr 2006, 13:52
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