Question

According to the National Agricultural Aviation Society (NAAS), without the use of crop protection products to control insects, weeds, and diseases, crop yields per acre will drop by more than 50 percent. The first aerial application of insecticide occurred in 1921, and it was a huge success. By contrast, in today's economy all aircraft that are classified as aerial applicators do more than just apply insecticide; today, they also spread seeds and apply fertilizer.

From the information given above, it CANNOT be validly concluded that:

• A. According to the NAAS, if crop yields per acre never drop by more than 50 percent, then crop protection products have been used to control insects, weeds, and diseases.
• B. In today's economy, any aircraft that cannot be used to apply fertilizer cannot be classified as an aerial applicator.
• C. In today's economy, if an aerial applicator is used, then it will be able to spread seed and apply fertilizer.
• D. According to the NAAS, if crop yields per acre drop by more than 50 percent, then crop protection products have not been used to control insects, weeds, and diseases.

Hint:

Check whether each option swaps and negates both sides of the passage's rule, or whether it just reverses the rule without negating it.

Answer 1

The Correct Option is D

Step 1: Write the passage as a rule.
The passage says: if crop protection products are not used, then yields drop by more than 50 percent. Call not using protection \(P\) and the yield drop \(Y\), so the rule is \(P \to Y\).

Step 2: Test option A against this rule.
Option A says: if yield never drops by more than 50 percent, then protection was used. That is \(\lnot Y \to \lnot P\), which is the contrapositive of the rule. A contrapositive is always true whenever the original rule is true, so option A follows and is not our answer.

Step 3: Test options B and C using the second sentence.
The passage also states every aerial applicator today spreads seed and applies fertilizer, not just insecticide. Option C simply restates this, so it holds. Option B is the contrapositive of that same fact (a craft that cannot apply fertilizer is not an aerial applicator), and a contrapositive always holds, so B follows too. Neither is our answer.

Step 4: Test option D.
Option D says: if yield drops by more than 50 percent, then protection was not used. That is \(Y \to \lnot P\), which reverses the direction of the rule instead of swapping and negating both sides. This is a converse, and a converse does not have to be true just because the original rule is true. Yield could drop by more than 50 percent for many other reasons even when protection products are used, such as drought, a new pest, or disease. So this cannot be validly concluded from the passage.

Final Answer:
Option D makes a converse error, so it is the one statement that cannot be validly concluded. \[ \boxed{\text{Option D}} \]