Because of a typographical error, the word "not" was dropped from an important sentence in a story about challenger Lawrence J. Hogan's plans to cut the budget if he defeats Prince George's County Executive Winfield M. Kelly Jr., in Tuesday election. Hogan, the story reported, has promised to use a "surgeon's knife" to cut "duplication of services and fat." and has said he will not reduce essential services.

Republican county executive candidate Lawrence J. Hogan claims to have in his possession a study that shows how he could cut as much as $43 million from the Prince George's County budget.

Hogan will not reveal who prepared the study for him, however. Nor will he list in detail the precise budget cuts that the document recommends, at least not until Nov. 8, the day after the election in which he is running against incumbent Winfield M. Kelly Jr.

Until then, Hogan said in an interview yesterday, the voters will have to take him at his word when he promises that next year, when and if he is elected, he will actually cut the $443 million budget, something that has never happened in county history.

"The voters," said Hogan, "will just have to trust me."

Hogan's treatment of the budget issue, and his plea for voters' trust, show one of the advantages that a challenger has over an incumbent in a political campaign. The challenger is free to talk about what he will do, hypothetically, not what he has done, concretely. As Hogan put it yesterday: "It's easy to be on the outside and say it."

As a polished, veteran campaigner, one who has been on the outside and the inside, Hogan says he understands the freedom that the challenger role gives him this year. He has also learned one of its dangers: saying too much.

"Let me tell you the practical problem," the former three-term congressman said yesterday. "Every time you say exactly where the budget can be cut, you alienate another group. They start spreading rumors about how you'll abolish the hospital commission or some other agency. I've already heard that there are notices up on some agency walls that I'll eliminate them. If you talk too much, you'll get in trouble."

Since early September, when Hogan began his campaign against Kelly, he has said repeatedly that he will cut the budget simply by eliminating what he calls the "waste, duplication of services and fat" in the county bureaucracy.He has said that he will use a "surgeon's knife" to do it, and will reduce essential services.

Hogan's attempts to cite specific examples of waste and duplication in the Kelly government have been modest, in terms of how much could be saved, and, in at least three instances, inaccurate.

At his first press conference after the primary, Hogan charged that Kelly had a sunroof constructed for his county-owned car at public expense. Hogan said this symbolized "a wasteful and luxurious attitude" the part of the county executive. Kelly later produced receipts to show that he paid for the sunroof with his own money.

During the first two televised debates between the two candidates, Hogan said the purchasing divisions of several county agencies should be consolidated. He said that more than $3 million could be saved simply by merging the police purchasing division with the general purchasing agency. The county budget shows, however, that only $112,000 is spent each year for the administration of police purchasing. The rest of the $3 million Hogan said could be saved actually went to the purchase of gasoline, clothing and repairs for the police fleet of cars.

At every forum at which Hogan and Kelly have both appeared, Hogan has charged that his opponent, in four years as county executive, has submitted budgets totaling $40 million more than what the County Council eventually approved. In fact, according to public documents, the council approved budgets larger than Kelly's proposal in three of the four years, with the only cut coming in fiscal year 1978 and amounting to about $4 million.

Hogan said yesterday that his information about Kelly's budget proposals came from Councilwoman Darlene White, the only Democratic office-holder in the county who has endorsed him. White could not be reached yesterday for comment.

Hogan has also said that money could be saved by consolidating the printing services in the county - there are now 18 separate printing presses in eight agencies - and by consolidating the data processing divisions in several agencies. The savings from these actions, by Hogan's calculations, would amount to more than $2 million a year.

The fiscal analysts in the Kelly administration concede the potential savings that could accrue from such consolidations. They argue, however, that consolidating the services of several autonomous or semiautonomous agencies, such as the school board, the park and planning commission and the Prince George's Community College, is not as easy as Hogan make it sound.

Even if Hogan were able to eliminate all the duplication of services that he has mentioned during the campaign and cut all the fat that he could find, Kelly fiscal advisers believe he would fall short of actually cutting the budget.

"It's a virtually impossible task," said Kelly aide Samuel Wynkoop yesterday. "We're working on a budget that will only increase 4 percent next year, and that's hard enough. To get it down to an actual cut would mean lopping off another $18 million."

According to Wynkoop's calculations, the budget preparations for next year will begin with a built-in increase of more than $35 million because of merit and cost-of-living salary increases for county employes and the inflated cost of county purchases. Thus, when Kelly speaks of holding the budget increase to 4 percent and Hogan promises to cut it, they are both talking about cutting it in real terms.

Hogan may be further burdened than Kelly in his effort to cut the budget because of his promise to send contract negotiations with county employes to binding arbitration, a procedure that Kelly charges would result in higher wage pacts for unions than collective bargaining would.

If the union gets a contract that we can't afford (as a result of binding arbitration)," Hogan said yesterday, "then we'll just have to cut it somewhere else. I think binding arbitration is the only fair way for employes who can't strike. I'm not going to change that belief just because it might be difficult."

Hogan said he was confident that he would be able to cut the budget next year because he would go into the job with the "right approach."

"It's an attitudinal thing," said Hogan. "If you get people to believe that the government can run just as efficiently with a smaller budget, we can do it, I'm sure. Why do you think so many county employes are supporting me? They know where the waste is, where the duplication is, and we'll find it. There are definitely offices that have surplus employes. The county executive's office has 42 - it could be cut to 30. It can be done, believe me."