American Realty Trust of Arlington trimmed its operating deficit from $4.2 million to $370,000 last year, and Chairman Thomas J. Broyhill said the real estate investment trust "should show earnings" in 1978.

Preliminary, unaudited results for the year ended Sept. 30 showed a net income of $94,000, (4 cents a share) including a $465,000 gain from the sale of property. In the prior year, American REIT lost $3.8 million despite a $453,000 gain from sale of real estate.

During the first quarter of its current year, the trust reported that a $1,372 million gain from property sales wiped out a $95,000 operating deficit, producing net profits of $1,276 million (58 cents) compared with $207,000 (9. cents) for the same period the previous year.

BDM Corp. of McLean reported that profits passed the million-dollar mark last year, climbing 53 percent to $1.025 million ($1.44 a share) from 670,000 ($1.06).

The firm, which provides systems analysis, planning and problem-solving services mostly in the defense contracting business, reported a 36 percent increase in revenues, to $32 million from $24 million.

At year end, BDMs backlog of contracts was $21.3 million, up from $14.3 million a year earlier.

The Arundel Corp., a Baltimore contruction, materials and real estate firm, reported its net income increased to $4.3 million ($2.65 a share) last year from $2.9 million ($1.78).

Arundel Chairman Henry J. Knott said the company had revenues of $3.1 million from continuing operations, compared with $2.9 million the previous year, due to improved results in the real estate and construction materials businesses.

For the three months ended Dec. 31, net earnings fell to $485,000 (32 cents) from $974,000 (97 cents), mainly due to two major construction jobs nearing completion.

The Student Loan Marketing Association - Sallie Mae - nearly doubled its earnings last year, allowing the government-sponsored company to declare a $3.75 per share dividend yesterday.

Sallie Mae reported that earnings increased to $4.3 million ($26.09 a share) from $2.2 million ($13.42).

A year ago a $1.50-a-share dividend was paid by Sallie Mae, which provides a secondary market in student loans by either directly buying student loans from their makers or by accepting student loans as collateral on loans that must be used to make more student loans.

With 152 educational and financial institutions participating in its program, Sallie Mae's total assets rose 25 percent last year, from $411 million to $512 million.