I graduated from an undergraduate program in May 2015 and was preparing to apply for my OPT. However, in July, my grandfather passed away and I was contemplating returning to India. My parents convinced me to stay on and complete an internship to gain experience. In mid-July, my grandmother was also hospitalized. In the meantime, I managed to find an internship but decided against staying as I wanted to spend time with my grandmother and family during this troubled time. But my parents were not at home and could not send me a return ticket until after the grace period had passed. I left the U.S. voluntarily 30 days after the grace period expired.
Now I am applying for a fresh F1 visa for graduate school. All other factors are satisfactorily covered - financial assistantship, choice of school and course. Will I be denied on the basis of a brief overstay? Also, on the DS-160, should I mention the overstay in the background security question that is asked towards the end of the form?
Note: I did not accrue unlawful presence and was not contacted by USCIS during those 30 days. I was not deported but left voluntarily.