78) Prime and Factor

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78) Prime and Factor

by ern5231 » Wed May 12, 2010 8:21 pm
P and Q are prime numbers and M,N are integers. PQ is a factor of MP+NQ. Which of the following must be true?
1) P is a factor of N
2) Q^2 is a factor of MP
3) P^2 is a factor of NQ

P.S None of the above is also an answer option

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by kstv » Wed May 12, 2010 8:34 pm
P and Q are prime nos
M and N are integers
MP + NQ has a factor PQ
only if M= Qa and N = Pb where a and b are constant
then MP+NQ = Qa*P+Pb*Q = PQ(a+b)
1) N= Pb so P is a necessarily a factor of N.
2) Possible but not necessary
3) Possible but not necessary

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by ern5231 » Sun May 16, 2010 6:26 pm
any more opinions?