abstract speed time data sufficiency - EXPERTS PLEASE HELP

[kaps786]

Hi Experts - I am having some difficulty with abstract data sufficiency questions.

Can you explain how one should approach these question types. What I mean, please see some questions below.

Question 1 below, particularly if someone can help explain.


A man went on a n miles trip. Its first 1/6 of the time was completed with a speed of r mile/hr. First 1/2 of the time was completed with a speed of 8 miles/hr. The first 1/3 of the time was completed with a speed of 12miles/hr. What is the man's average speed?

（1）n=20
（2）r=4

How should you approach a problem, like this...?? In all these problem types... some of the parameters like time, distance etc are not numbers but relatively expressed such as ..1/6 of the time etc...which I find difficult to comprehend and interpret.

Can someone illustrate an approach for these systematically


Another type of DS problem from GMATprep to explain what I mean...

During a 40-mile trip, Marla traveled at an average speed of x miles per hour for the first y miles of the trip and at an average speed of 1.25x mph for the last 40-y miles of the trip. The time that Marla took to travel the 40 miles was what percent of the time it would have taken her if she has traveled at an average speed of x miles per hour for the entire trip?
1) x = 48 2) y = 20

Would be really greatful if some experts can help

[neelgandham]

During a 40-mile trip, Marla traveled at an average speed of x miles per hour for the first y miles of the trip and at an average speed of 1.25x mph for the last 40-y miles of the trip. The time that Marla took to travel the 40 miles was what percent of the time it would have taken her if she has traveled at an average speed of x miles per hour for the entire trip?
1) x = 48 2) y = 20

I will try and explain you one question and will leave the other one for you to work with. I have split the question into individual statements and then provided a mathematical representation of the statement.

Marla traveled at an average speed of x miles per hour for the first y miles of the trip
So, time taken to travel y miles at x mph= (y/x) hours - (I)

and at an average speed of 1.25x mph for the last 40-y miles of the trip
So, time taken to travel next 40-y miles at 1.25x mph = (40-y)/(1.25x)- (II)
Total time taken to travel 40 miles = (y/x)+((40-y)/(1.25x)) - from (I) and (II)

The time that Marla took to travel the 40 miles was what percent of the time it would have taken her if she has traveled at an average speed of x miles per hour for the entire trip?

If she has traveled at an average speed of x miles per hour for the entire trip, then total time taken to travel 40 miles = 40/x.
From the question If (40/x) = (k/100)*[(y/x)+((40-y)/(1.25x))], where k > 0, find the value of k.
(40/x) = (k/100)*[(y/x)+((40-y)/(1.25x))]
40 = (K/100)*[(y/1)+((40-y)/(1.25*1))] - Multiply both sides with x
40/[(y/1)+((40-y)/(1.258*1))] = k/100
k = 4000/[(y/1)+((40-y)/(1.25*1))], so we need the value of y to find the value of k.

1) x = 48

Oops, Insufficient!

2) y = 20

perfect! We can answer the question

Answer B

[Anurag@Gurome]

Hi Experts - I am having some difficulty with abstract data sufficiency questions.

Can you explain how one should approach these question types. What I mean, please see some questions below.

Another type of DS problem from GMATprep to explain what I mean...

During a 40-mile trip, Marla traveled at an average speed of x miles per hour for the first y miles of the trip and at an average speed of 1.25x mph for the last 40-y miles of the trip. The time that Marla took to travel the 40 miles was what percent of the time it would have taken her if she has traveled at an average speed of x miles per hour for the entire trip?
1) x = 48 2) y = 20

Would be really greatful if some experts can help

Time would have taken if speed was x mph, T = 40/x hour
Time taken in current situation, t = [(y/x) + (40 - y)/(5x/4)] hour
= [(y/x) + 4*(40 - y)/(5x)] hour
= [(5y + 160 - 4y)/(5x)] hour
= [(y + 160)/(5x)] hour

Required percentage = 100*(t/T) = 100*[(y + 160)/(5x)]/(40/x )
= 100*[(y + 160)/200] = (y + 160)/2

Thus the percentage depends upon y not on x.

Hence statement 1 is not sufficient whereas statement 2 is sufficient.

The correct answer is B.

[GMATGuruNY]

During a 40-mile trip, Marla traveled at an average speed of x miles per hour for the first y miles of the trip and at an average speed of 1.25x mph for the last 40-y miles of the trip. The time that Marla took to travel the 40 miles was what percent of the time it would have taken her if she has traveled at an average speed of x miles per hour for the entire trip?
1) x = 48 2) y = 20

Here's a more conceptual approach, since you asked.

Time and rate are RECIPROCALS.
x = the REGULAR speed.
1.25x = the FASTER speed.
1.25x = (125/100)x = (5/4)x.
5/4 the rate implies 4/5 the time.
Thus:
The time needed at the FASTER speed is equal to 4/5 the time needed at the REGULAR speed.

The question stems asks for the following ratio:
(time needed when some of the distance is traveled at the faster speed):(time needed if the entire distance is traveled at the regular speed).
Since the question is asking only for a ratio, the actual speed and the actual distance are not needed.
To calculate the requested ratio, all we need is the answer to the following question:

What FRACTION of the distance was traveled at the faster speed?

To illustrate:
Let the total distance = 40, the regular speed = 4mph, and the faster speed = 5mph.
Time needed to travel the entire 40 miles at the regular speed = 40/4 = 10 hours.
Time needed to travel half the distance at 4mph and half the distance at 5mph = (20/4 + 20/5) = 9 hours.
Faster time:regular time = 9:10.

Let the total distance = 80, the regular speed = 20mph, and the faster speed = 25mph.
Time needed to travel the entire 80 miles at the regular speed = 80/20 = 4 hours.
Time needed to travel half the distance at 20mph and half the distance at 25mph = (40/20 + 40/25) = 18/5 hours.
Faster time:regular time = (18/5):4 = (18/5):(20/5) = 18:20 = 9:10.

Notice that changing the actual distance and the actual rates does not affect the ratio.
In each case, since half the distance is traveled at the regular speed and half the distance is traveled at the faster speed, the ratio of the times is the same:
9:10.

Onto the statements at hand:

Statement 1: x=48
The rate is irrelevant: regardless of the rate, the time needed at the faster speed is 4/5 the time needed at the regular speed.
INSUFFICIENT.

Statement 2: y=20
Thus, half the distance was traveled at the faster speed.
SUFFICIENT.

The correct answer is B.