5003 Praxis Practice Test Practice Question
The houses on a certain road have either no garage, a one-car garage, or a two-car garage. Five houses have no garage. One-third of the remaining houses have a one-car garage. If 18 houses have a two-car garage, how many houses are there on the road?
Correct Answer: 32 houses
Rationale: To find the total number of houses, start by noting the houses with no garage (5). The remaining houses consist of those with either a one-car garage or a two-car garage.
Let \( x \) be the total number of houses. The remaining houses after accounting for the no-garage houses are \( x - 5 \). Given that one-third of these remaining houses have a one-car garage, we can express this as \( \frac{1}{3}(x - 5) \).
The problem states that there are 18 houses with a two-car garage. Thus, the equation becomes:
\[
\frac{1}{3}(x - 5) + 18 = x - 5
\]
Solving this leads to \( x = 32 \).
Other options are incorrect because they do not satisfy the established relationships and totals from the problem. For example, if there were 30 houses, the calculations would not align with the given number of two-car garages or the proportion of one-car garages. Only 32 houses correctly balances all conditions.
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