When the president of Sweet Briar College announced that the school would close forever this summer, many women burst into tears.

But then a common refrain began to echo through the small Virginia school’s close-knit alumnae: Not if I can help it.

A Web site appeared, complete with slogans (“Think is for girls” and “Save Sweet Briar” ) shared happy memories of life on the pristine Southern campus, and one very ambitious goal.

James Jones, the president, said the board had unanimously voted to close because of “insurmountable” financial challenges.

When asked point-blank by alumnae what it would cost to keep the school open, he had an equally direct answer: $250 million.

So the alumnae decided to raise $250 million.

By Thursday morning, people had signed up to give almost half a million dollars (plus one anonymous pledge of $1 million.)

Women began digging into Jones’s background, finding criticism of his tenure at Trinity College in Connecticut. One checked with the local planning office to look for signs of an impending sale of some of the campus’ more than 3,000 acres of beautiful countryside. Some talked with lawyers. Others contacted current and former board members.

They unleashed a social media campaign, by turns earnest, defiant, and mischievous.

More than 4,000 women are involved, said 2012 graduate Alexandra Mebane, in a fast-moving effort to keep the college open, at least until the current students can graduate. “We strongly believe something has occurred there that doesn’t add up,” she said. “There’s no reason for this to come out of thin air.”

Kelly Gardner Headd, a 1993 graduate, said, “Many of us are suspicious about the motivations behind the decision. We are asking: cui bono?  Who benefits? Did the board and/or president have an as yet unacknowledged incentive to make this decision and with such suddenness? And to keep alums in the dark until it was too late for alternatives to closing to be considered?

“There is much grief, anger and bewilderment in our community. There is also such a feeling of betrayal as the decision to close Sweet Briar was made by board members who are graduates of the college. These are individuals one hoped would fight to the last breath to save our school.

“As one of my fellow alums put it on a conference call the other night, it feels like a cherished relative you thought would long outlive you has died.”