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Brindac2
Hi,

Statement 1:

Car B averaged a speed of 40 miles per hour for the entire trip.

Car B travelled at 40 miles in 60 minutes.

so, in 30 minutes, 20 miles is crossed by Car B. While , Car A could have travelled a distance of 80 miles.

Thus, A is nearest to the destination. Hence, Sufficient. Agree.

Statement 2 :

This statement provides information of Car A speed at the time of crossing i.e 80 mph. But that doesn't conclude that the speed of Car A was constant at this rate.

Even if we assume here that Car A speed was constant at 80, then the car which is nearest to destination becomes B. In this case, the answer we come up with Statement 1 & Statement 2 are different; which is not allowed. The answer to both statements, if they are truly independent, should be one.


So, the final answer should be A.

Hi, I am not an expert to comment extensively on this. But still, I would be immensely happy to respond back.

Firstly, Speed was not constant and they have given average speed till crossing, as this is sufficient to ascertain the distance travelled by that vehicle A. With the total distance being constant , the remaining distance is covered by vehicle B can be found out easily.

Secondly, the question asks which car is closer to the destination, taking statement 1 alone with the basic info from question, we have arrived at an answer, and that answer seems to address the question asked.

While taking into consideration, the question and statement 2 in isolation, we are able to answer the question : which car is closer to destination ? . Even though, this answer might not resonate with the earlier answer. But, we have been able to arrive at an answer based on the cards we have at hand.

Hope I was able to clarify your doubts.

I believe in data sufficiency question, the merit of the statement at that point should be considered while evaluating the validity.

Even I am curious to look into the solution, after ur seeing ur comment. Let’s wait and see how things turn up.
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ExpertsGlobal5
Cars A and B are stationed in “Townville” and “Cityburg”, respectively. The two cities are connected by parallel highways and are 100 miles apart. The two cars begin their journeys simultaneously, moving in opposite directions, each heading towards the other car’s point of departure. If the two cars cross each other after 30 minutes, which car is closer to its destination city at the point of crossing?

(1) Car B averaged a speed of 40 miles per hour for the entire trip.
(2) When the two cars crossed each other, car A had averaged a speed of 80 miles per hour.


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Let their speeds be \(a\) and \(b\) respectively at the point of crossing.

\(\frac{a}{2}+ \frac{b}{2}= 100 \)

\(a+b=200\)

If we can know which of \(a\) or \(b\) is greater we can answer the question.

The one with greater speed at the point of crossing will be closer to it's destination.

(1) Car B averaged a speed of 40 miles per hour for the entire trip.

Since distance is \(100\) therefore car B took a total of \(2.5\) hours for the whole journey.

However at the point of crossing we do not know what was it's speed.

We cannot assume it was moving at a constant speed of 40 m/h for the entire trip.

INSUFF.

(2) When the two cars crossed each other, car A had averaged a speed of 80 miles per hour.

This directly gives us \(a= 80\)

We know at the point of crossing

\( a+b=200 \)

Thus at the point of crossing \(b=120\)

Thus at the point of crossing B is closer to it's destination.

SUFF.

Ans B

Hope it helped.
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ExpertsGlobal5
Cars A and B are stationed in “Townville” and “Cityburg”, respectively. The two cities are connected by parallel highways and are 100 miles apart. The two cars begin their journeys simultaneously, moving in opposite directions, each heading towards the other car’s point of departure. If the two cars cross each other after 30 minutes, which car is closer to its destination city at the point of crossing?

(1) Car B averaged a speed of 40 miles per hour for the entire trip.
(2) When the two cars crossed each other, car A had averaged a speed of 80 miles per hour.
Explanation:

Let the distance traveled by car A be X miles when the two cars crossed each other.
Then, the distance traveled by car B would be (100 – X) miles.
The time taken by the two cars to meet is 30 minutes.
We need to find which car was closer to its destination city at the point of crossing.
In simple words, we need to find which car traveled faster or traveled greater distance, before the two cars crossed.

Statement (1)

The given information pertains to the speed of just one of the two cars.
Average speed for the entire trip is mentioned for one car and no information is provided regarding the speed of the other car before the two cars crossed each other.
It is not possible to determine with certainty which car is closer to its destination.

Since it is not possible to determine with certainty which car is closer to its destination city at the point of crossing. Hence, Statement (1) is insufficient.

Statement (2)

Distance X traveled by car A = speed x time = 80 x 1/2 = 40 miles.
Distance traveled by car B = 100 – X = 100 – 40 = 60 miles.
Thus, car B traveled a greater distance and is closer to its destination.

Since car B traveled a greater distance at the point of crossing, it is closer to its destination. Hence, Statement (2) is sufficient.

B is the correct answer choice.
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