BTGmoderatorDC wrote: ↑

Sun Oct 31, 2021 6:27 pm

A parking garage has spaces for cars and vans only. If there is a total of 118 vehicles in the garage, how many of them are vans?

(1) If 14 more vans are driven into the garage, there will be twice as many vans as cars in the garage.

(2) If x vans and y cars are driven into the garage, there will be an equal number of vans and cars in the garage.


OA A

Source: Princeton Review

Given: A parking garage has spaces for cars and vans only. There is a total of 118 vehicles in the garage,
Let C = the number of cars
Let V = the number of vans
We can write: C + V = 118

Target question: What is the value of V?

Statement 1: If 14 more vans are driven into the garage, there will be twice as many vans as cars in the garage
We can write: V + 14 = 2C

We now have the following system of two different linear equations:
V + 14 = 2C
C + V = 118
Since we COULD solve the system for C and for V, we could answer the target question (although we would never waste valuable time on test day doing so)
Statement 1 is NOT SUFFICIENT

Statement 2: If x vans and y cars are driven into the garage, there will be an equal number of vans and cars in the garage.
We can write: V + x = C + y
There are several values of x, y, V and C that satisfy statement 2 (and the given information, C + V = 118). Here are two possible cases:
Case a: V = 59, C = 59, x = 3 and y = 3. In this case, the answer to the target question is V = 59
Case b: V = 58, C = 60, x = 3 and y = 1. In this case, the answer to the target question is V = 58
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent