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Simple answer: $12,000.

Technically, a person may claim exempt only if he had no tax liability last year and expects to owe no tax in the current year.

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What is the under age 19 mean regarding the dependent EXEMPT limit?  18 and under or 19 and under qualifies.   Thanks Hal_AI
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First NO ONE should ever claim exempt UNLESS they are sure they had NO tax liability the prior tax year AND they are sure they will have NO tax liability in the current year ... since you can never be 100% sure of the second part the wise thing to do is simply increase the # of allowances claimed on the W-4 ...either follow the worksheet  or have them enter Single and 4 allowances on line 5.
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That is, there are no exceptions for age, student status or dependent status.  The same rule applies for everyone.
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State requirements may be different.