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My textbook tells me the following structure is 2,2,5-trimethylpentane. I try to change the parent group in different ways so as to maximize the number of substituent groups, but I think the maximum number of substituent groups for any arrangement is 3 - so my answer is 2,2,4-trimethylpentane. Am I wrong in thinking this?

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There are 2 methyl groups on the second carbon of the main chain, and 1 methyl group on the fourth carbon of the main chain, so 2,2,4-trimethylpentane is correct! If there was a methyl group on the 5th carbon of a pentane, it would be a hexane, so it would not make sense to name it the way your book did.

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