Are you a Female Project Manager? How do you succeed in a male dominated industry?

I wish that was true Pench!

I've found in the competitive world of Project Management, your gender can be a real handicap!

One way to ‘play the game’ by using misogynists’ own arrogance against them. For example, in many work situations women do most of the essential work while their male bosses profit from their efforts. This arrangement works because society has trained women to focus so much on being accepted and liked that they will tolerate incredibly unfair situations. This focus is so strong that women fail to realize the immense power they hold, since most businesses would come to a screeching halt if they were to quit.
So, let’s say you’re a woman in an organization where you can’t advance due to misogyny. You know you’re doing most of the work but aren’t being fairly compensated for it. In this situation you could seek out new responsibilities to improve your resume. Don’t let the men know you’re doing this to grow, however; let them think you’re just being ingratiating. One day you can make the company an ultimatum – give you a particular position at a particular salary, or you’ll resign. The men will probably try to placate you with vague promises of a promotion sometime in the future or a partial salary increase. If they don’t accede to your demands, leave the company and take all your knowledge and experience with you.

I'd say that 75% estimate is accurate when it comes to men applying for jobs. In fact, it's probably a bit less. As Larry says, many times a job's true requirements are combined with desired traits. Recruiters know these likely won't be met, but they figure there's no harm in asking anyway.

I’ve seen these number too in this report:
https://leanin.org/tips/mvp

They provide this explanation:
Women and men ascribe their success to different things. Men typically attribute their success to innate qualities and skills, while women often attribute success to external factors such as “working hard,” “getting lucky,” or “help from others.” Women and men also differ when it comes to explaining their failures. When a man fails, he attributes it to situational factors like “didn’t practice enough” or “not interested in the subject.” When a woman fails, she is more likely to attribute it to lack of ability.
As a result, women gives themselves less credit and don’t have confidence as men.