The following question consists of six statements a, b, c, d, e, and f followed by four groups of three statements each. Identify…

Question

The following question consists of six statements a, b, c, d, e, and f followed by four groups of three statements each. Identify the group or groups in which the third statement logically follows from the first two statements.

Statements:

a. Every car is a bus

b. Some buses are trains

c. Several trains are not buses

d. A lot of cars are not trains

e. Many cars are trains

f. No car is a train

1. A. a e c
2. B. a e b (Correct answer)
3. C. a d f
4. D. a d c

Correct Answer

Option B — a e b

Detailed Solution & Explanation

The correct answer is a e b.

Key Points

• Test each group by asking whether the third statement must be true given the first two.
• Take group a e b: *Every car is a bus* and *Many cars are trains*. The cars that are trains are also buses, so there exist buses that are trains — which is exactly statement b, *Some buses are trains*.
• The inference is valid, so a-e-b is the required group.

Additional Information

• Group a e c fails: from *every car is a bus* and *many cars are trains* nothing follows about trains that are not buses.
• Group a d f fails: *a lot of cars are not trains* leaves open that some cars are trains, so *No car is a train* does not follow.
• Group a d c fails for the same reason — a particular negative about cars cannot establish a claim about trains generally.
• The reliable technique is to look for a shared middle term (here *cars*) that carries the property across to the conclusion.

*Ministry of Papers worked solution. The Commission has not yet published the official key for this paper; this answer will be reconciled with it on release.*