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# digit ps from briozeal post

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Manager
Joined: 05 Oct 2005
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digit ps from briozeal post [#permalink]  19 Jul 2006, 17:05
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0% (00:00) correct 0% (00:00) wrong based on 0 sessions
hello
plz explain your reasoning on this one
thanks

Problem 3: What 2 digit number (which is a integer) is the product of its digits
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when there is a will there is a way

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Manager
Joined: 04 Jul 2006
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Maybe I'm missing something, but I think that there exists no such number:
You can rewrite every (positive) two-digit number, which is an integer, (for example 36) as x10+y, (x, y are integers <10|in this case x would be 3 and y would be 6).

For every two-digit number: x10+y > xy. (This is trivial because of y<10).

Hence, no number exists that fulfill the property x10+y=xy.
Intern
Joined: 11 Jul 2006
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Agree with that...there is no two digit no which is equal to the product of its digits.
Manager
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arunsanand wrote:
Agree with that...there is no two digit no which is equal to the product of its digits.

here is the link to the post but i don 't understand the approach used

http://www.gmatclub.com/phpbb/viewtopic ... =remainder
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SVP
Joined: 24 Sep 2005
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mand-y wrote:
arunsanand wrote:
Agree with that...there is no two digit no which is equal to the product of its digits.

here is the link to the post but i don 't understand the approach used

http://www.gmatclub.com/phpbb/viewtopic ... =remainder

buddy, the problem was misread ..it must be: what is the two-digit number which is twice the product of its digits.
Let's look at the solution provided in the link:
------------
Solution1:Let x be the digit in ten's place and y be the digit in unit's place.
From question stem: 10x + y = 2xy
Therefore, x = y/2(y-5)
Since x and y are digits of a 2-digit number, x and y are positive integers.
So, y must be greater than 5 and also y must be even. Try the first even number greater than 5 => 6
If y = 6, x = 3 --> 2-digit number = 36
-------------
from 10x+y= 2xy --> y must be even coz 2xy and 10x are even
since x=y/2(y-5) --> y must be > 5 coz if y<=5 --> y-5<= 0--> x <=0 coz y/2 is always > 0

=> the bold part.
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