1. Statements :
Some gears are wheels. All wheels are brakes.
Conclusions :
I. No brake is gear
II. Atleast some gears are brakes.
Answer is 2 as some gears are wheels and hence since all wheels are brakes- those some must be brakes too.
2. Statements :
No month is a year. No year is a second.
Conclusions :
I. All months are seconds.
II. No second is month.
Answer is 4 as neither can be derived from the given statements.
3. Statements :
No plane is hill. Some hills are towns.
Conclusions :
I. No town is plane.
II. Some towns are plane.
Answer is 4 as neither can be derived from the given statements.
4. Statements :
All metals are liquids. All liquids are gases.
Conclusions :
I. All metals are gases.
II. Atleast some gases are liquids.
Answer is 1 as all metals are liquids and all liquids are gases imply that all metals are gases. II need not be true as there can be a case that no liquids exist.
5. Statements :
Some cities are towns. Some villages are cities.
Conclusions :
I. Atleast some villages are towns.
II. No village is a town
Answer is 4 as neither can be derived from the given statements. Some villages are cities and some cities are towns. But unless the "some" in both statements are the same, I needn't be true.