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06 Feb 2010, 10:56
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Just got the number properties guide from MGMAT and already have a question on the first section on divisibility of primes:
They said one rule (this is said in both Knewton and MGMAT) that if a number is a factor of y and a factor of x, it's also a factor of y+x.
In this question: if 8 is not a factor of g, is 8 a factor of 2g?
The answer they gave is that there's not sufficient information. However, if you apply the rule above, 2g is just g+g (both factors of 8), so the only way that 8 can be a factor of 2g is if 8 is also a factor of g. So, doesn't this mean 8 is NOT a factor of 2g?
They said one rule (this is said in both Knewton and MGMAT) that if a number is a factor of y and a factor of x, it's also a factor of y+x.
In this question: if 8 is not a factor of g, is 8 a factor of 2g?
The answer they gave is that there's not sufficient information. However, if you apply the rule above, 2g is just g+g (both factors of 8), so the only way that 8 can be a factor of 2g is if 8 is also a factor of g. So, doesn't this mean 8 is NOT a factor of 2g?
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06 Feb 2010, 12:03
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Let's start with rule: if a number is a factor of y and a factor of x, it's also a factor of y+x.
if a number, let's say z, is a factor of x and y, we can say:
x = nz and y = mz , where n and z are integers.
Then x + y = nz + mz = (n+m)z ---> (n+m) is an integer and z is a factor of (n+m).
Now let's consider your example: if 8 is not a factor of g, is 8 a factor of 2g?
we can't apply the rule because 8 is not a factor. See examples,
1) g = 9: 8 is not a factor of g and not a factor of 2g (18).
2) g = 12: 8 is not a factor of g but is a factor of 2g (24 = 3*8)
if a number, let's say z, is a factor of x and y, we can say:
x = nz and y = mz , where n and z are integers.
Then x + y = nz + mz = (n+m)z ---> (n+m) is an integer and z is a factor of (n+m).
Now let's consider your example: if 8 is not a factor of g, is 8 a factor of 2g?
we can't apply the rule because 8 is not a factor. See examples,
1) g = 9: 8 is not a factor of g and not a factor of 2g (18).
2) g = 12: 8 is not a factor of g but is a factor of 2g (24 = 3*8)
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06 Feb 2010, 12:04
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the rule you mentioned does NOT apply to the "Not factor statement". Cobnsider the example (let g=4):
8 is not factor of 4 (g)
but 8 is a factor of 8 (2g)
8 is not factor of 4 (g)
but 8 is a factor of 8 (2g)
