WASHINGTON (AP) _ Virginia's governor, James S. Gilmore, meant to shock his audience this month when he reported that as many as one-third of would-be teachers in the state flunked a national test of basic reading, writing and mathematics.

If it was bad news for Virginia, it was worse for the nation. Virginia has the country's highest cutoff score for the Praxis I, used in 20 states to screen teacher college candidates and beginning teachers. Scarcely more than half the students who took the test nationwide would have made the Virginia cut.

``Virginia students would be doing much better than the national average,'' said Charlotte Solomon, in charge of the Praxis examinations for the Educational Testing Service, a private company that supplies the tests to states. ``It begs the question of whether it's good enough.''

Around the country, state education officials are asking whether tests of general knowledge and of specific subjects are rigorous enough to ensure that able people become teachers. The issue has risen in importance because of widespread efforts to raise standards for what children should know and be able to do.

For some states, it means setting standards for the first time.

Last October in New Hampshire, the board of education voted to adopt Praxis I starting this fall after years of opening the profession to anyone with a college teaching degree who could find work. Democratic Gov. Jeanne Shaheen vetoed legislation that would have required the tests for teachers who already have jobs.

Some 35 states use Praxis I or more advanced tests in the Praxis series used to certify graduates for general knowledge, professional skills and subject knowledge. Some states have their own tests.

Explanations vary on why scores are low, but poor pay tops the list. ``It clearly holds back who it is that's entering,'' said Gordon M. Ambach, executive director of the Council of Chief State School Officers.

Teaching has become less attractive for women and minorities since barriers to other, more lucrative and prestigious jobs have been lowered.

Education officials also point out that not everyone with low test scores goes on to teach or even get an education degree.

In Pennsylvania, education officials are beginning to raise the bar for a number of tests. Among those being examined is a 120-question, general knowledge test for beginning teachers that covers social studies, math, literature and the arts, and science.

``We have a relatively high pass rate, but as we look at the exams and we look at the cut stores, we're not convinced that it is a meaningful exercise,'' said Michael Poliakoff, a deputy secretary of education. Nearly 91 percent of would-be teachers who took the general knowledge test last fall passed it.

But most of the test-takers scored just about at the national average of 657 on a scale of 600-695. The state passing score is 644, close to that of several other states. The highest cut score of any state is 649 in Maine, New Jersey, New York and Rhode Island.

Like other critics, Poliakoff says the national average would look good if the test were demanding. But people are asked to do such things as put World War I, the start of the Great Depression, the New Deal and the Korean War in the right order.

The testing service doesn't say Praxis I results would compare with those on an SAT, a widely given test for college admissions.

``It's only partially true'' that Praxis is an easier test, Solomon said, explaining that the tests have different aims.

But new Georgia and Delaware standards, comparable to those of other states, give some clue. State officials allow the SAT and ACT, another admissions test, to be used instead of Praxis 1. A total SAT score of 1000, with at least 520 on the mathematical and 480 on the verbal part, is acceptable.

The average SAT score for 1997 high school graduates was 505 verbal and 511 math. Those who said they will pursue education degrees had scores of 485 verbal and 479 math. Math majors had scores of 549 verbal and 623 math. Language and literature majors had scores of 609 and 546.

But the standards often run afoul of the need to staff schools, especially in hard-to-fill rural and inner city schools.

North Carolina had to back off from higher standards several years ago. Mississippi is debating waivers for its cutoffs. Florida has allowed waivers.

Shortages also worry the same Virginians who advocate tough standards.

``You can begin to wonder what's going to happen down the road when more and more people turn away from preparing to teach,'' said Thomas A. Elliott, an assistant superintendent of education.