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Gcd!


surya167

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What is the greatest common divisor of positive integers m and n ?

 

1) m is a prime number

2) 2n = 7m

 

 

GCD(m,n) is equal to the product of all similar prime factors of m and n.

 

(1) "m is a prime number"

 

"n" can either have m as a factor or not, so INSUFFICIENT.

 

(2) "2n = 7m"

 

This only tells us that n has one more 7 in its prime product than m and that m has one more 2 in its prime product as n. Finally, all other prime numbers appear the same number of times in m and n.

 

This leaves open an inifinite number of possible GCD's. INSUFFICIENT

 

 

(1) and (2)

 

If m is prime, then it has to be 2, since m has to have one more 2 in its prime product than n.

 

If m is 2, then n is 7, and GCD(m,n) = 1

 

Thanks, lsr! I was doing the GCD for 2n and 7m. :)

 

C

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My Ans is C

 

1. n can be any value, so insuff

 

2. if 2n = 7m, then we know that n has to be a factor of 7 and m has to be a factor of 2.

so 2n = 2.7.k

and 7m = 7.2.l where k,l are integers

To find out the gcd we have to find other common factors of k, l.

So this stmt by itself is insufficient

 

Combinin both statements, we know that m is prime and that it has to be a factor of 2.

so m = 2, n = 7

GCD = 14 so sufficient

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