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by sanju09 » Sat Feb 06, 2010 5:54 am
abhasjha wrote:What is the greatest common divisor of positive integers m and n?

1) m is a prime number

2) 2n=7m
(1) If m is a prime number, then it may or may not be a prime factor of n. Hence the greatest common divisor may be either m or m n. Moreover, m and n are also not known. Insufficient

(2) If twice of one positive integer is 7 times another positive integer, then the former must have 7 as its factor, or n has 7 as one of its factor, for sure, whereas, m may or may not have 7 as one of its factor. Also, that the later must have 2 as its factor, or m has 2 as one of its factor, for sure, whereas, n may or may not have 2 as one of its factor. So, if n = 7 p and m = 2 q for some positive integers p and q, then their greatest common divisor is the greatest common divisor of the positive integers p and q that we don't know. Insufficient

Taken together

If m is prime, then q is 1, and the greatest common divisor of p and 1 is p. We don't know what's p. Still insufficient

[spoiler]E[/spoiler]
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by ajith » Sat Feb 06, 2010 8:05 am
abhasjha wrote:What is the greatest common divisor of positive integers m and n?

1) m is a prime number

2) 2n=7m
1.) if m is a prime number the greatest common divisor of m and n can be either 1 or m
It is insufficient to conclude what is the gcd

2) 2n = 7m

N is a multiple of 7 and m is a multiple of 2 insufficient to calculate GCD

Now, If we combine these two

m=2 and n=7 and GCD is 1; Sufficient

C according to me
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by abhasjha » Mon Feb 08, 2010 12:20 am
OA is C
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by papgust » Mon Feb 08, 2010 1:22 am
ajith wrote: 1.) if m is a prime number the greatest common divisor of m and n can be either 1 or m
It is insufficient to conclude what is the gcd

2) 2n = 7m

N is a multiple of 7 and m is a multiple of 2 insufficient to calculate GCD

Now, If we combine these two

m=2 and n=7 and GCD is 1; Sufficient
Ajith,

Can you explain statements I and II with a bit more in detail? Esp., the concept behind it.
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by sanju09 » Mon Feb 08, 2010 1:34 am
sanju09 wrote:
abhasjha wrote:What is the greatest common divisor of positive integers m and n?

1) m is a prime number

2) 2n=7m
(1) If m is a prime number, then it may or may not be a prime factor of n. Hence the greatest common divisor may be either m or m n. Moreover, m and n are also not known. Insufficient

(2) If twice of one positive integer is 7 times another positive integer, then the former must have 7 as its factor, or n has 7 as one of its factor, for sure, whereas, m may or may not have 7 as one of its factor. Also, that the later must have 2 as its factor, or m has 2 as one of its factor, for sure, whereas, n may or may not have 2 as one of its factor. So, if n = 7 p and m = 2 q for some positive integers p and q, then their greatest common divisor is the greatest common divisor of the positive integers p and q that we don't know. Insufficient

Taken together

If m is prime, then q is 1, and the greatest common divisor of p and 1 is p. We don't know what's p. Still insufficient

[spoiler]E[/spoiler]
Oh yes!!

If m is prime, then q is 1, to allow us take m = 2, now; and also if 2 n = 7 m, n = 7, and the greatest common divisor of m and n is 1.

[spoiler]sorry...it's C[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



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