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The gross income test considers the dependent's taxable income. The support test considers all income, taxable and nontaxable.
Total support items include
Compare the dollar value of the support provided by the taxpayer with the total support the person received from all sources.
In figuring a person's total support, include tax-exempt income, savings, and borrowed amounts used to support that person. Tax-exempt income includes certain social security benefits, welfare benefits, nontaxable life insurance proceeds, Armed Forces family allotments, nontaxable pensions, and tax-exempt interest.
Here is an example from the IRS Pub 501
Your brother's daughter takes out a student loan of $2,500 and uses it to pay her college tuition. She is personally responsible for the loan. You provide $2,000 toward her total support. You cannot claim an exemption for her because you provide less than half of her support.
I sincerely XXXXX XXXXX is helpful,
Thanks for the reply. I saw this information before. I believe it is all in Pub 501. As a loan co-signor, I most certainly have some personal reponsibility for the loan. It is on our (wife and I) credit reports, and the legal small print on the note indicates that we can be required to pay the debt (e.g. if the student borrower does not), without going through any drawn out legal process.
I am afraid "personally responsible" is too general to help me out.