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# The three-digit integer mkk is the sum of the two-digit

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Current Student
Joined: 11 May 2008
Posts: 551
The three-digit integer mkk is the sum of the two-digit  [#permalink]

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25 Jul 2008, 18:19
The three-digit integer mkk is the sum of the two-digit integers mk and nk, where k, m, and n are the digits of the integers. Which of the following must be true?
I. m= 1
II. n = 9
III. k= 5
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III

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Director
Joined: 20 Sep 2006
Posts: 630

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25 Jul 2008, 18:40
IMO D,

k + k = k (in unit place) the only possible value of k is 0.
VP
Joined: 17 Jun 2008
Posts: 1279

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25 Jul 2008, 21:49
arjtryarjtry wrote:
The three-digit integer mkk is the sum of the two-digit integers mk and nk, where k, m, and n are the digits of the integers. Which of the following must be true?
I. m= 1
II. n = 9
III. k= 5
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III

when we form equations we get
90m+9k-10n=0
inorder this to be true : only possible set of integers is {m,k,n}={1,0,9}
hence I and II

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Its Now Or Never

Re: unknown integers &nbs [#permalink] 25 Jul 2008, 21:49
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# The three-digit integer mkk is the sum of the two-digit

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