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A 7mm induration from a Mantoux test in an HIV positive client is interpreted as a positive reaction because this population is considered immunocompromised. In individuals with HIV, a 5mm induration or greater is indicative of a positive test result. This criterion acknowledges the diminished ability of individuals with HIV to mount a strong immune response to the tuberculosis antigens that the test evaluates.

In the context of the other answers, a size of less than 10mm would be negative for someone who is not immunocompromised but not applicable here due to the client's status. Similarly, a response that is less than 15mm is also irrelevant, since the relevant threshold for an HIV positive person is lower at 5mm. The mention of a false positive result related to a previous BCG vaccination does not apply here; while the vaccination can complicate interpretation in certain situations, the 7mm result is still sufficient to classify as a positive reaction in an HIV positive patient.