WASHINGTON — Any reporter who’s written about the federal budget knows that there’s a surefire solution to every problem. It’s called “fraud, waste and abuse.” You want to end budget deficits? Just eliminate all the “fraud, waste and abuse” in the $4 trillion budget. The same is true for cutting taxes or raising spending. Attacking fraud and waste is virtuous and dispenses with the hard political work of making unpopular choices.

It’s a fantasy, of course. There isn’t enough “fraud, waste and abuse” — or we can’t get at it — to evade the difficult choices. But we cling to the mythology because it makes us seem “responsible” and reduces the budget problem to purging sloth and policing misdeeds.

I was reminded of that recently when The Washington Post published a fascinating front-page story headlined “Pentagon hid study revealing $125 billion in waste.” The article, meticulously reported by Bob Woodward and Craig Whitlock, disclosed that a Defense Department study had found that the Pentagon was “spending almost a quarter of its $580 billion budget on overhead and core business operations such as accounting, human resources, logistics and property management.”

These jobs need doing, but it seems that the generals are being overwhelmed by accountants and property managers. If we could squeeze $125 billion out of the Pentagon’s annual budget, there’d be plenty of money to spend on true military needs. Indeed, the report asserts that the savings could cover the costs for 50 Army brigades. It sounds straightforward.

It isn’t.

On inspection, it turns out that the estimated savings of $125 billon are spread over five years, from fiscal 2016 to 2020. This changes the numbers dramatically. Instead of annual savings of 22 percent of the defense budget ($125 billion out of $580 billion), the plausible cuts are closer to 4 percent ($125 billion out of the roughly $3 trillion projected in defense spending from now until 2020).

The confusion over whether the estimated savings apply to one year or five is the weak spot in an otherwise excellent piece of reporting. Whitlock and Woodward do say that the savings occur over five years, but they don’t emphasize the point. Moreover, there are mixed messages. Much of their discussion of costs focuses on the annual budget. A prominent graphic shows the annual defense budget and then claims that the Pentagon report “identified a way to save $125 billion.”

What would a “reasonable reader” conclude from the muddled evidence? By “reasonable,” I mean curious and intelligent readers who are not experts and are somewhat casual in their reading. These people, I think, might get the wrong idea. They’d come away thinking that the potential annual savings are enormous and that reducing waste would ensure an adequate military.

Of course, we should do everything possible to reduce waste, and the incoming Trump administration should take a second look at the report. But some outside budget experts are unimpressed. “It’s a somewhat speculative study,” says Michael O’Hanlon of the Brookings Institution. The targets for savings are more “back-of-the-envelope calculations” than detailed roadmaps for change.

Some “waste” reflects complexity. A few years ago, the Army tried to replace its Bradley Fighting Vehicle; it abandoned the project as too complicated, after spending $18 billion, recalls Todd Harrison of the Center for Strategic and International Studies. The new study complains that the Pentagon has more than 700,000 civilian and contract workers to support 1.3 million active-duty troops. But these workers, says Harrison, are often the cheapest way to get a job done.

Like O’Hanlon, Harrison doubts that the study’s full savings can be achieved. Many proposals would founder on congressional opposition and management practicality. “Can you do the same work with fewer people?” he asks. “If so, who should be cut? The study doesn’t answer that.”

These questions are obviously more than academic. The Pentagon says it needs more spending than the existing budget ceilings allow. Some experts agree. O’Hanlon argues that defense spending should increase by nearly $50 billion annually over existing levels. How should we respond to the various threats: terrorism, cyberwarfare, Russia, China?

Whatever the answer, we shouldn’t fool ourselves into thinking that the contradiction can be resolved by eliminating vast amounts of waste. If we wish to reduce defense spending, we have to cut the military’s size and capabilities. If we wish to expand the military, we need to pay for it.

The underlying struggle pits the Pentagon against the welfare state. Over the decades, national priorities have shifted dramatically. As late as 1990, defense spending constituted 24 percent of the federal budget and 5 percent of the economy (gross domestic product). In 2015, defense was 16 percent of the budget and 3 percent of GDP — and these figures were declining. This is one war the Pentagon is clearly losing.

Robert Samuelson is a columnist with The Washington Post.