Automobile A is traveling at two-thirds the speed that Automobile B is traveling. How fast is Automobile A traveling?

BTGModeratorVI wrote: ↑

Sun Jul 19, 2020 1:49 pm

Automobile A is traveling at two-thirds the speed that Automobile B is traveling. How fast is Automobile A traveling?

(1) If both automobiles increased their speed by 10 miles per hour, Automobile A would be traveling at three-quarters the speed that Automobile B would be traveling.

(2) If both automobiles decreased their speed by 10 miles per hour, Automobile A would be traveling at half the speed that Automobile B would be traveling

Answer: D
Source: Princeton Review

Given: Automobile A is traveling at two-thirds the speed that Automobile B is traveling.
Let A = Car A's speed
Let B = Car B's speed
So, we can write: A = (2/3)B

Target question: What is the value of A?

Statement 1: If both automobiles increased their speed by 10 miles per hour, Automobile A would be traveling at three-quarters the speed that Automobile B would be traveling.
Car A's new speed = A + 10
Car B's new speed = B + 10
So, we can write: A + 10 = (3/4)(B + 10)
We already know that: A = (2/3)B
IMPORTANT: Since we have a system of 2 different linear equations with 2 variables, we COULD solve the system for A and B (but we'd never waste valuable time on test day doing so)
So, we COULD answer the target question with certainty.
Statement 1 is SUFFICIENT

Statement 2: If both automobiles decreased their speed by 10 miles per hour, Automobile A would be traveling at half the speed that Automobile B would be traveling
Car A's new speed = A - 10
Car B's new speed = B - 10
So, we can write: A - 10 = (1/2)(B - 10)
We already know that: A = (2/3)B
Once again, we have a system of 2 different linear equations with 2 variables, which we COULD solve for A and B.
Statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent