Knesl wrote:
hi,
can somebody help me with following question? I would need the explanation.
To arrive at its destination on time, a bus should have maintained a speed of \(V\) kmh throughout its journey. Instead, after going the first third of the distance at \(V\) kmh, the bus increased its speed and went the rest of the distance at \((1.2)*V\) kmh. If, as a result, the bus arrived at its destination \(X\) minutes earlier than planned, what was the actual duration of the trip?
1. \(V = 60\)
2. \(X = 20\)
(C) 2008 GMAT Club - m10#8
* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient
Thanks!!!
A trick used by GMAT is that they give you similar looking data in the two statements (e.g. in this question, value of one variable given in each statement) and you feel that either each alone will be sufficient or both together. But analyzing the data shows that only one statement is sufficient, the other is not.
The bus covers 1/3 of distance at speed V. The rest 2/3 at speed 1.2V
___________________________
.....V........ ----------1.2V----------
Usual time for the journey is, lets say, T hours, but it arrived in T - X/60 hours. (X is in minutes so you have to change it to hours)
Now, out of the usual T hours, in first 1/3rd of the journey, the bus takes T/3 hours. In rest 2/3rd of the journey, the bus usually takes 2T/3 hours.
During this particular journey, the bus took T/3 hours for the first 1/3rd of the trip (since it traveled at speed V) but for the rest 2/3rd of the trip, it took less time since it traveled at greater speed of 6V/5 (Convert decimals to fractions)
If speed becomes 6/5 of original, time taken will become 5/6 of original.
So time taken to travel 2/3rd of the trip is 5/6 * 2T/3 = 5T/9 hours
In this trip, the total time taken = T/3 + 5T/9 = 8T/9
So the X/60 hours that are saved are equal to T - 8T/9 = T/9
X/60 = T/9
Statement 1: Just V doesn't help. You need D too to get the value of T. Not sufficient.
Statement 2: Knowing just X is sufficient to get T as seen above. Sufficient.
Answer (B).