“In the news” or “on the news”

Solution 1:

The answer is C, "on the news".

This is an example a completely different usage of "on the news" to the one described by Benjamin Harman. In this case, "on the news that..." means "as a result of the news that..."

i.e. The news that the company would have to recall over 30,000 tires was the trigger that led to company's stock tumbling.

Solution 2:

In the news...

This refers to when someone or some event is widely discussed in that subset of media we call "the news."

"Barrack Obama was in the news." This means that Barrack Obama was discussed widely among news outlets, including television, radio, print, etc.

On the news...

This refers to when someone or some event is being reported on a television program that is classified as a news program.

"Barrack Obama was on the news." This means that Barrack Obama appeared on a news show broadcast on television.

Q: The company's stock tumbled _____ the news that it would have to recall over 30,000 tires that were produced in 2004.

The preposition would be "on."

First, when one is tripped by something, one stumbles "on" it, not "in" it. For example, "I stumbled on a stick and broke my arm."

Second, using "on" to mean "upon hearing," just flip the sentence to see:

1. On the news that it would have to recall over 30,000 tires that were produced in 2004, the company's stock tumbled.

or

2. In the news that it would have to recall over 30,000 tires that were produced in 2004, the company's stock tumbled.

A simplified example:

1. On the news of him cheating, Mary broke up with Steve.

or

2. In the news of him cheating, Mary broke up with Steve.

It becomes pretty clear just by sound that the first is right: "on."