Hi, there! This looks like a fun question. Prompt
: If a car traveled for 2 hours from 7:00 till 9:00, at what speed was the car moving at 8:00?
Notice, this is a tricky prompt. The question is asking for something known in physics as the instantaneous velocity --- how fast the object is going at a particular moment in time. When you're driving, the speed displayed on your speedometer at any particular moment is the instantaneous velocity at that moment. It's easy to find the instantaneous velocity if you happen to have a working speedometer, but it's not easy to calculate
the instantaneous velocity. In fact, the branch of math designed to calculate stuff like instantaneous velocity is Calculus, which is well beyond the scope of the GMAT. Unless there's some very special conditions, we will not be able to determine an instantaneous velocity. Statement #1
: During the journey the car traveled 120 km
This allows us to calculate the average velocity ---- 120km/2hr = 60 km/hr. On average, the car went 60 km/hr. That does not mean that the car was going at exactly 60 km/hr during every moment of the trip. In a real-life trip, if I drive 120km in 2 hours, there will be times I'm going faster on the highway, times I am going slower on local streets, and even times my instantaneous velocity is zero when I am stopped at a stop sign or red light. The overall average will be 60 km/hr, but that does not allow one to determine the instantaneous velocity at any particular interval. Statement #1, by itself, is insufficient
. Statement #2
: The car traveled at constant speed throughout the journey
First of all, this is a wildly wildly make-believe unrealistic scenario that could never happen in the real world (and therefore, probably not something the real GMAT would put forward as Statement -- GMAC has a relatively strong reality-principle.) Nevertheless, this is the statement here, so let's go with it. If the speed is constant throughout the trip, then the speed at any particular interval is the average speed for the trip. Unfortunately, with Statement #2 alone, we have no idea what the distance is, and no way to calculate the average velocity, so we cannot give a numerical answer to the prompt. Statement #2, by itself, is insufficient
. Combined Statements #1 & #2
From #2, we have instantaneous velocity = average velocity, and from #1, we have average velocity = 60 km/hr. Combining those, we have: instantaneous velocity at 8 pm = 60 km/hr. We are able to give a definite numerical answer to the prompt, so the combined statements are sufficient
For free for further practice, here's a more realistic average speed DS problem:http://gmat.magoosh.com/questions/927
The question at that link, when you submit an answer, will be followed by a video explanation. Each of Magoosh
's over 800 questions has its own video explanation.
Does all this make sense? Please let me know if anyone reading this has any questions.
Magoosh Test Prep