Pre-print, Working paper: In most countries, female and low income students are still largely under-represented in top science graduate programs. Relying on a unique database on French Grandes Écoles graduate programs and their competitive entrance examinations, this paper reveals that the possibility of repeating and retaking entrance examinations several times contributes significantly to the strong over-representation of high income male students in these very selective programs. Female students appear to be less sensitive to small differences in prestige between programs and more reluctant to persevere in competitive environments.