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# What is the greatest common divisor of positive integers m

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Manager
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What is the greatest common divisor of positive integers m [#permalink]

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16 Jun 2006, 22:39
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What is the greatest common divisor of positive integers m and n?

C1. m is a prime number

C2. 2n = 7m
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16 Jun 2006, 23:02
Can't say. Should be E.

What if n is a multiple of m? Not addressed in either of the choices.
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16 Jun 2006, 23:18
I will go with D.

Both statements individually are sufficient.
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Re: DS: Number Properties (GMATPrep problem) [#permalink]

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17 Jun 2006, 04:24
mrmikec wrote:
What is the greatest common divisor of positive integers m and n?

C1. m is a prime number

C2. 2n = 7m

I'll go with C.

1 - Insufficient. we don't know anything about n.

m=3
n=3 Greatest divisor is 3

m=7
n=2 Greatest divisor is 1

2 - insufficient, multiple values for this equation

Together - 2n = 7m.....given that 2n is even, 7m must also be even. However, we know that m is prime..therefore m must be 2 in order for 7m to be even.

m must be 2, and n must be 7.

C.
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Re: DS: Number Properties (GMATPrep problem) [#permalink]

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17 Jun 2006, 13:00
tl372 wrote:
mrmikec wrote:
What is the greatest common divisor of positive integers m and n?

C1. m is a prime number

C2. 2n = 7m

I'll go with C.

1 - Insufficient. we don't know anything about n.

m=3
n=3 Greatest divisor is 3

m=7
n=2 Greatest divisor is 1

2 - insufficient, multiple values for this equation

Together - 2n = 7m.....given that 2n is even, 7m must also be even. However, we know that m is prime..therefore m must be 2 in order for 7m to be even.

m must be 2, and n must be 7.

C.

I got B but now I see where i went wrong. Great explanation tl372!

originally i though

if 2n=7m, then

2n = some multiple of 7, 2, and any integer
conversely,
7m = some multiple of 2, 7, and any integer

so can you conclude that 7 is the greatest common divisor?

or do you mean that the "any integer" can be equal and thus the greatest common divisor...

but

so if 2n = 140 then, 2, 7, 10
7m = 140, 7, 2, 10

GCD is 10. you could have an infinite number of GCD depending on the value of the integer selected.

But if m is prime and 7m is even, m=2. and the GCD is 7.
Re: DS: Number Properties (GMATPrep problem)   [#permalink] 17 Jun 2006, 13:00
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