GMAT Quant Chapter 8: Rate Problems Flashcards
What element from Quant Chapter 7 must we always ensure before solving Rate-Time-Distance problems?
Ensure the units have been compatible so that all are in the same version of time or distance, e.g. km or miles, seconds, or hours etc.
Name the 8 question types of Rate-Time-Distance questions
- Elementary
- Average
- Converging
- Diverging
- Round Trip
- Catch-up
- Relative
- If / then
What are the 4 different types of converging questions?
- Both objects leave same time
- Objects leave different time
- One object faster speed
- One object faster relative speed
What are the 2 standard variations of the catch up question?
- Faster object, same location start, must catch up and pass beyond slower object
- Faster object, behind start location, catch up or catch up and pass slower object
Why are miles per gallon questions actually simple and easy?
They are rate problems
mpg * g = m
What are the 3 essential relationships in the rate problems?
- Distance is directly proportional to rate and time
- Rate is inversely proportional to time and directly proportional to distance
- Travel time inversely proportional to rate & directly proportional to distance
How do we solve an average rate problem?
Rate is the ratio of two different quantities.
We must use the total time travelled and the total distance travelled. Aggregate them first and then calculate rates.
do not add different rates together
What is a converging rate problem and what does this mean?
Converging rate problems are when two objects move towards each other.
This means the total distance travelled will be the sum of the two objects travelled.
What fact is implicit when two objects leave in a converging rate problem?
When they meet, if travelling at constant rates, they will have travelled the same time.
Use variable t for both equations, set them equal to each other and solve.
How do we reflect the difference in travel times for a converging rate problem where two items leave at different times?
Why is this counterintuitive?
The object that leaves first has t + the difference in travel time
The object that leaves second has variable t for travel time
The object that leaves first has time added to their t variable.
How do account for different speeds in a converging rate problem?
The slower object’s speed is labelled r
The faster object’s speed is labelled r + the difference in speeds
How do we solve a converging rate problem when one speed is relatively faster than the other object
When the first object is x time as fast as the second object,
2nd object rate: r
1st oibject rate: xr
When solving diverging rate problems, what do we know about the total distance?
In diverging rate problems the total distance travelled in the question is the sum of the distances of the individual objects
What do we know about round trip problems made on the same path?
the total distance travelled is 2x the distance from point a to point b
What piece of information is the clue to solving catch up rate problems?
When the faster object catches the slower object, the distance each object has traveled will be equal
