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DNA question

Thanks for the link Peter. Not good odds to prove anything are they.
6th Cousin 0.01%Variable

Been trying to prove if a pacific fella was my grandfather. He died in 1975. He didn't have any kids but he does have a 6th//7th cousin here in Australia and I was wondering if we did a DNA if it might at least prove if im on the right road or not.
I've had two people matching me as 3rd and 4th cousins both looking for there fathers. The first one matched me as a 4th cousin and is in Australia. We have an idea who he was but we were looking for another person to take a DNA test to prove it, sadly he died anyway so it would be another person to give the sample.

The other one like your grandfather was adopted, she had her mother's name but she was also looking for her father. She was a 3rd cousin match, but she was a closer match to another 3rd cousin of mine and sure enough her father was first cousin to her. I think they have met now.

It's worth doing one test just to rule it out.

If someone was a 6th or 7th cousin to my grandfather and if he and I had a DNA done would it show we are related?

I recently had a DNA test done. The cost was around £60.00 The results were for me a little disappointing, but did throw out some information giving 1st, 2nd, 3rd, 4th, 5th DNA related matches by giving a percentage of the likelihood of particular people being a relative or distant relative. I am in contact with three people I would never have known and more pop up via the DNA site. If you want to make contact you are able to use that DNA site. So you do not have to correspond if you do not want to.
You can of course pay a little more and maybe search for a really good testing site that gives better results. You'd have to do your home work though. Don't forget what one DNA site provides to one person, may or may not be less or better for another...we are all different :)
DNA testing is not straightforward. There are three different tests you can take, each of which is used differently.

Autosomal DNA tests are really only useful for the last 6 generations or so, because the ancestors' genes get watered down. But autosomal does indicate what sort of relationship there could be and how distant it is.

YDNA is only for chaps; ladies can get their father or brother to take it for them if they are sure the chap really is their father or brother. YDNA traces the direct male line going back quite some time, and if that someone you are tracing is a chap, he might have the same YDNA as you ... if you are a chap.

Everyone has mtDNA, but it is only passed by women. A direct female line can be traced back many generations, and a total stranger can match your mtDNA exactly, showing that you have a common female ancestor. The modern full sequence mtDNA is far more reliable than the older HVR1 and 2 tests, but is also expensive. The full sequence test identifies a common female ancestor in the last 400 years with 95% certainty.

This all means that in your case you could use YDNA or mtDNA to test for a relationship, and if you get a match you will have to fill in the gaps using traditional genealogy. I wouldn't think autosomal DNA testing is any use at all to you.