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# MN is a two-digit integer. When MN is divided by (M+N), it

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MN is a two-digit integer. When MN is divided by (M+N), it [#permalink]

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08 Oct 2003, 09:42
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MN is a two-digit integer. When MN is divided by (M+N), it leaves a quotinent of 3 and a remainder of 7. Find MN.
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Joined: 29 Aug 2003
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08 Oct 2003, 13:10
10M + N = (M+N)*3 + 7
=> 3M + 3N + 7 = 10M + N
=> N = (7M-7)/2 ....... (1)
Also, for N to be a single digit number, 7M-7 < 20 => M < 27/7

So, M can be one of 1, 2 or 3

Only M=3 satisfies (1) above.

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08 Oct 2003, 23:05
amarsesh wrote:
10M + N = (M+N)*3 + 7
=> 3M + 3N + 7 = 10M + N
=> N = (7M-7)/2 ....... (1)
Also, for N to be a single digit number, 7M-7 < 20 => M < 27/7

So, M can be one of 1, 2 or 3

Only M=3 satisfies (1) above.

My approach:

10M+N=3M+3N+7
7M-7=2N
7(M-1)=2N, so N is a multiple of 7, but less than 10 since it is a digit. Therefore, N=7 and M=3.

37 is correct.
Re: PS: MN   [#permalink] 08 Oct 2003, 23:05
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