Self-study
Support Each new car in the lot at Rollway Motors costs more than $18,000. ███ ███ ██ █████ ███ ████ ██ ███ ██ ████ █████ ███ █████ ████ ████ ███████ █████ ██ █ ███ ██ █████████ ███ █████ ███████ ██████ ███ ████████ ██ ██ █ ████ ███ ████ ██ ████ ████ ███ █████ ████
Method of Reasoning
The author makes a valid argument based on the contrapositive of two statements.
new car → more than 18k
10+ years old → less than 5k
Conclusion:
between 5k and 18k → NOT new car and NOT 10+ years old
Let’s look for two conditional premises and a conclusion that asserts if we do not meet the necessary conditions of the two conditional premises, then we do not meet the sufficient conditions of those two premises.
23.
The pattern of reasoning in █████ ███ ██ ███ █████████ █████████ ██ ████ ███████ ██ ████ ██ ███ ████████ ██████
a
Each apartment above ███ ██████ █████ ██ ███ ████████ ███ ████ ████ ███ █████████ ███ ███ ██████████ █████ ███ ██████ █████ ████ █████ ████ ███ █████████ █████ ███ █████████ ██ ███ ██████ █████ ██ ███ ████████ ███ ███████ ███ █████████
This is an invalid argument, so it can’t parallel the valid argument in the stimulus. (A) is invalid because it’s possible some apartments on the fourth floor have more than two bedrooms or fewer than two. (A) could have been correct if the conclusion said, “any apartment that has exactly two bedrooms is on the fourth floor.”
b
Each apartment above ███ ██████ █████ ██ ███ ████████ ███ ███ ██ █████ █████████ ███ ██ █████████ █████ ███ ██████ █████ ███ ████ ████ ███ █████████ █████ ███ ██ ███ ██████████ █████████████ ██████████ ███ ██ ███ ██████ █████ ██ ███████
(B) doesn’t reach a conclusion that uses the contrapositive of both conditional premises. The conclusion is based only on the contrapositive of the second premise. That premise says the following:
below the fourth floor → NOT more than two bedrooms
This is enough to support the conclusion, which asserts that all of the building’s three bedroom apartments are NOT below the fourth floor. Although this is a valid argument, it doesn’t parallel the structure in the stimulus.
c
No apartment above ███ ██████ █████ ██ ███ ████████ ███ █████ ████ █████ █████████ ███ ███ ██████████ █████ ███ ██████ █████ ████ █████ ████ ███ █████████ █████ ██ █████ ███ ██████████ ██ ███ ████████ ████ ███████ ███ █████████ ████ ███ ██ ███ ██████ ██████
This reaches a valid conclusion based on the contrapositive of both premises.
Above fourth floor → NOT fewer than 3 bedrooms
Below fourth floor → fewer than 2 bedroom
Conclusion:
exactly 2 bedrooms (fewer than 3 and NOT fewer than 2) → fourth floor (NOT above fourth floor and NOT below fourth floor)
d
No apartment above ███ ██████ █████ ██ ███ ████████ ███ ████ ████ ███ █████████ ███ ████ █████████████ ██████████ ████ ██████████ █████ ██ ███ █████████ ██ ███ ████████ ███ █ ████████ ██ ██ ██ ███ ██████ █████ ██ ██████
This doesn’t reach a conclusion based on the contrapositive of both premises. Rather, the conclusion is based on connecting the two conditional premises:
above fourth floor → NOT more than 2 bedrooms
balcony → 3 bedrooms
Conclusion:
balcony → NOT above fourth floor
That’s a valid conclusion based on connecting the premises to each other, but it doesn’t parallel the structure in the stimulus.
e
Each apartment above ███ ██████ █████ ██ ███ ████████ ███ ████ ████ ███ █████████ ███ ████████ ███ ██ ██████ ██████████ ██ ██ █████ ███ ██████ ██████ █████ ██ █████ ██ ███ ██████ █████████ ██ ███ █████████ ██ ████ ████ ████ ████ ███ █████████
This doesn’t reach a conclusion based on the contrapositive of both premises. Rather, the concusion is based on connecting the two premises together:
above fourth floor → more than 2 bedrooms
vacant → above fourth floor
Conclusion:
vacant → more than 2 bedrooms
This is a valid argument based on connecting the two premises to each other, but this doesn’t parallel the structure in the stimulus.