WASHINGTON — The national push to increase the number of Americans who have college degrees is enriching at least one key beneficiary: the College Board, the nonprofit organization that’s best known for administering the SAT.

Eleven states and the District of Columbia each have agreed to pay the College Board anywhere from several hundred thousand dollars to more than $1 million a year to test students in hopes of boosting their college-enrollment numbers. The tests cost students nothing. The College Board is actively promoting its products in other states.

These deals are likely to further increase the College Board’s net revenues, which hit $65 million in 2010 — the last year for which the figure was available from tax filings — up from $53 million the year before. The test supplier pays a quarter of its employees at least $230,000 a year, while its president, Gaston Caperton, earns more than $1 million annually — almost double what he made in 2005 — and has a $125,000 expense account.

“They’re a very profitable nonprofit organization,” said Brad MacGowan, a college counselor at Newton North High School in Newton, Mass., a Boston suburb. “They always seem to be coming up with a new product or service to push testing into younger grades or make states give the SAT to every student.”

Ten states — Arkansas, Connecticut, Delaware, Florida, Georgia, Indiana, Maine, New Mexico, Oregon and Texas — and the District of Columbia pay for the College Board’s PSAT test to be given to their students at no cost.

In addition, three states — Delaware and Idaho since last year and Maine since 2005 — require and pay for all high school students to take the SAT. Last school year, Texas required school districts to pay for the exam for every student who wanted to take it, although it eliminated the program this year because of budget cuts.

Officials in Delaware and Idaho said the legislation requiring all students to take the SAT passed with no input from the College Board. But documents show that the group has a lobbying presence in a number of other states.

In Massachusetts, the College Board paid a lobbying firm $24,000 last year to support “general outreach on education issues, specifically Advanced Placement, PSAT and college-readiness matters,” according to lobbyist disclosure forms. Last year in Indiana, a College Board lobbyist pushed for a bill to allocate $500,000 for ACT/SAT test preparation. And the College Board, which also administers advanced-placement exams, has tried to make AP classes mandatory in every California high school.

“They’re out there freewheeling, doing whatever they want, doing it however they want to do it, and no one is telling them ‘no,’ ” said Kenneth LaValle, a Republican in the New York state Senate and the chair of itsHigher Education Committee.

The College Board acknowledged that it often talks with policymakers.

“We regularly speak with state education officials and district administrators about how our programs and services can help them increase college readiness,” College Board spokeswoman Kathleen Steinberg said.

Nationally, in the Class of 2011, more than 1.6 million high-school seniors took the SAT, a 30 percent increase from a decade ago. The test costs $49. Sending SAT scores to up to four colleges is free, after which it costs a student $10.50 for every additional college. Rush delivery is another $30 per school. AP exams cost $87 each, and students took 3.1 million of these tests in the 2009-10 school year.

Caperton’s salary increase since 2005 could have paid for the PSAT to be given free to almost 34,000 students. And the College Board’s revenues in excess of expenditures last year were enough to have provided a refund to every student who paid full price to take the SAT.

The College Board said it put its earnings toward new products, services and advocacy. Last year, for instance, it spent $54.2 million on fee waivers for low-income students.

Some higher-education officials have criticized the SAT, calling it a narrow measure of college readiness. Others have charged that it favors students from wealthy school districts. A small but growing number of colleges are moving away from requiring standardized-test scores for admission.

Legislators, though, hope that offering the SAT and PSAT for free will improve college-going rates.

“I think those programs can be really valuable in that they emphasize a college-going culture,” said Robert Laird, former undergraduate admissions director for the University of California, Berkeley. But Laird added that if a student is required to take one of the exams and does poorly, such programs also can backfire and discourage students.