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PR and MN are 2-digit positive integers, where P, R, M, and [#permalink]
01 Aug 2008, 02:14

PR and MN are 2-digit positive integers, where P, R, M, and N are digits of the two numbers, and are different from each other. If the tens' digit of sum of PR and MN is M, which of the following must be true? I. M<9 II. R+N>9 III. P>8 A. I only B. II only C. III only D. I and II E. I, II and III

Re: incomplete positive integers [#permalink]
03 Aug 2008, 00:10

arjtryarjtry wrote:

PR and MN are 2-digit positive integers, where P, R, M, and N are digits of the two numbers, and are different from each other. If the tens' digit of sum of PR and MN is M, which of the following must be true? I. M<9 II. R+N>9 III. P>8 A. I only B. II only C. III only D. I and II E. I, II and III

say x=10p+r and y=10m+n => x+y= 10(p+m)+r+n

p+m=m when r+n > 9 hence II is must now carry from r+n is 1 hence p+m+1 =10a+m a is any number is possible when p=9 and m <9 => III and I are must

hence I,II and III are must IMO E _________________