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GCF question

by ildude02 » Fri Jun 20, 2008 8:56 am
if the expression #(a, b)# is defined to be the sum of a and b divided by the GCF of a and b, what's the value of #(6, x)#

(i)x is a positive odd integer not equal to 1.

(ii) The GCF of 6 and X is 1/7 the sum of 6 and x.

The way I solved this was, 6 has factors of 3 and 2. And if X is an odd integer greater then 1, it cannot have 2 as a factor. So the greatest common factor will be 3. I would appreciate your thoughts on GCF and your mode of solving the question.
Last edited by ildude02 on Fri Jun 20, 2008 10:55 am, edited 1 time in total.
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by Ian Stewart » Fri Jun 20, 2008 9:49 am
I'd be curious to see the whole question- it's a DS question, I take it.

You're right that 2 and 3 are factors of 6, but they aren't the only positive factors: 1 and 6 are also factors. And you're correct that if x is odd, then the gcf of 6 and x cannot be even. That still leaves two possible values for the gcf: 1 and 3. If x is a prime larger than 3, for example, the gcf of x and 6 will be 1 (and there are other cases as well where the gcf will be 1 -- if x is any odd number which is not divisible by 3, in fact). If x is an odd multiple of 3 (e.g. 21, 33, etc), then the gcf will be 3.
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by ildude02 » Fri Jun 20, 2008 10:54 am
Even though I came up with the INSUFF answer, I missed to consider prime numbers. Arithmetic involving multiples, LCM, Primes, GCF etc always trick me where I spend more time then usual.

I took examples like x= 3 and x= 9 to come up with anser=> #(6, X)= 6+3/3 = 3 and 6+9/3 = 5. But it's good that you made me realize I didn't consider primes.

My bad, I updated the question to include the second option as well to help everyone answer the DS in the proper way.
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by navalpike » Tue Jun 30, 2009 9:36 pm
So.......what is the answer? I come up with C but does anyone have the OA or did I miss it in the discussion?
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by tohellandback » Tue Jun 30, 2009 10:25 pm
is the OA E?

if the expression #(a, b)# is defined to be the sum of a and b divided by the GCF of a and b, what's the value of #(6, x)#

(i)x is a positive odd integer not equal to 1.

(ii) The GCF of 6 and X is 1/7 the sum of 6 and x.

1)NOT SUFF: x=2, value is 4
x=3 value is 3
2)NOT SIFF: x can be 8,15 or 36

combining
x can be 15 or 36

NOT SUFF
Last edited by tohellandback on Wed Jul 01, 2009 7:14 am, edited 2 times in total.
The powers of two are bloody impolite!!
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by tryin700 » Wed Jul 01, 2009 2:08 am
IMO ans B
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by rahulg83 » Wed Jul 01, 2009 2:43 am
statement 2 is sufficient...we have been give ratio of GCF and sum of two numbers. Whatever the numbers be, the ratio will remain the same
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