Strategies, Sample Questions, and Random Ramblings.
July 19, 2015
Honestly, a rate is exactly the same thing as a ratio. You are simply comparing two numbers with GMAT rates. However, because GMAT rates typically are based on some unit of time the question types are a little different than the ratio question types.
Most often this is some output per unit of time:
miles per hour meter per second sales per year
However, rates can also be between other things:
sales per customer window per building customers to table
Ratios can be used to show this relationships between other ratios.
You can use cross multiplication to solve.
135 miles = x
As you can see the easiest way to look at a rate is in terms of a fraction. Again, this is pretty much identical to a ratio. You are really just replacing the “to” in a ratio with “per” in a rate. Otherwise, pretty much all of the techniques that were discussed in the ratios section will apply here as well.
So, how is this different from ratios? As we said, primarily because of the time measurement there are different question types.
Before we get into the questions we must learn one formula:
Many people try to remember all combinations of this formula for each problem, but you being the smart GMAT taker will only have to remember this one knowing that it is easy to rearrange to get what you want.
Average rate questions are the first type. The key to these questions is to think of total distance and total time.
If Bob drove 150 mile at 50 miles per hour and another 150 miles at 60 miles per hour, what is his average speed?
Undoubtedly, many people will answer 55 as it seems logical. However, we are going to think in terms of total distance and time.
Total distance is easy at 150 + 150 = 300 miles
Total time we will have to calculate by figuring out the time for each leg of the trip and adding them together. First, rearrange the rate formula to this:
For the first leg we have this:
and for the second:
Now, with a total of 5.5 hours we can calculate the rate:
This may seem counter intuitive, but as demonstrated above, the fact that there is a different amount of time spent at each speed means this is a weighted average.
You can take a simple average of the speeds if you are traveling for the same amount of time. Traveling 3 hours at 50 miles per hour and 3 hours at 60 miles per hour will give you an average speed of 55 miles per hour.
If you travel for different amounts of time at different speeds, the problem becomes a weighted average problem, which we already know how to solve.
Another type of rate problem is a combined rate problem. This occurs when you have two objects moving toward each other, away from each other, or in the same direction.
Here are the keys to remember:
Greg R., client, New York City
Emil C., client, Singapore
Chris S, client, New York City