A train runs over a straight route from town A to town D. It is schedu

Question

A train runs over a straight route from town A to town D. It is scheduled to depart town A at 7am and arrive at town D at 2pm, with 10 minute stops in towns B and C. The train’s top speed is 60mph. The entire length of the route is 320 miles. Will the train arrive on time?

(1) The train experiences a 30 minute delay in town B in addition to its scheduled stop.

(2) The train travels at its top speed for exactly 75% of the trip.

ske · Accepted Answer

ANSWER E TOTAL TIME 7 HOURS STOPPAGE 20 MINS AFTER SUBTRACTION WE WILL GET 6 HOURS 40 MINS TOTAL JOURNEY 320 MILES TOP SPEED DOES NOT MEANS ACTUAL SPEED ,ITS BASICALLY A PEAK SPEED WHICH A TRAIN CAN ATTAIN . FROM A SUBTRACTING 30 MINS ,WE WILL GET 6 HOURS 10 MINS , WHICH MEANS TRAIN HAS TO COVER JOURNEY AT THE SPEED OF 51 MILES PER HOUR TO COMPLETE THE JOURNEY, ITS NOT GIVEN SO ANS A IS INSUFF POINT 2 75 % OF THE JOURNEY = 240 MILES BALANCE 80 MILES ,WE DON'T KNOW THE EXACT SPEED, SO B INSUFFICIENT OA MUST BE E GIVE KUDOS FOR MOTIVATION :-D

GMATinsight · Answer

Total Distance = 320 Miles
Total Time = 7 hours (7 AM to 2 PM) = 7*60 = 420 minutes
Time of Break = 2*10 = 20 minutes
Travel time to cover 320 Miles = 420 - 20 = 400 Mins
Max. Speed = 60 mph
Min speed required throughout to travel 320 miles in 400 mins = 320*60/400 = 48 mph

Question : Is Time taken to cover distance of 320 miles = 400 minutes ?

Statement 1 : The train experiences a 30 minute delay in town B in addition to its scheduled stop. 
Time taken by train when it travels the complete distance at max speed = 320*60/60 = 320 mins
including 10 mins break, total time = 320+20 = 340 Mins
Maximum delay acceptable = 420 - 340 = 80 mins
i.e. a train can reach on time even with 80 mins delay if it travels at top speed for all the time
30 mins delay may cause delay or on time journey. Hence,
NOT SUFFICIENT

Statement 2 : The train travels at its top speed for exactly 75% of the trip. 
75% of Trip = 320*75/100 = 240 miles
Time to travel 240 miles at Top speed = 240/60 = 4 hours = 240 mins
But Min speed is unknown which may or may NOT have caused any delay, Hence
NOT SUFFICIENT

Combining the two statements : 
240 mins exhausted to travel 240 miles
Remaining travel time = 400-240 = 160 mins
Remaining distance = 320-240 = 80 miles
Speed required to travel remaining distance in remaining time to be on schedule = 80*60/160 = 30 miles/hr
But Minimum Speed is unknown. Hence
NOT SUFFICIENT

Answer: Option E

HardWorkBeatsAll · Answer

(D) - each alone is sufficient. And happily, no one on the train will miss their meetings

7 am (A) ---------------- 10 min (B) ------------- 10 min (C) --------------- 2 pm (D) Time available (without any delays) = 7 hours - 20 mins = 6.66 hours or 6 (2/3) hours (mixed fraction). (A) -> Time is reduced to 6 hours 10 mins because of 30 min delay. i.e. Time available = 6 (1/6) (mixed fraction). Speed (max) = 60 mph. Time taken at this speed is - 320/60 = 5 hrs 20 min. So, time available is greater than time taken at max speed. Train reaches in time. Sufficient. (B) -> Dist covered in 75% = 3*320/4 = 240 miles Time taken for this 75% = 240/60 = 4 hours Remaining track = 320 - 240 = 80 miles Remaining time = 6(2/3) - 4 hours = 2(2/3) hours (mixed fraction = 2 hours 40 min). Note that the 30 min delay is NOT to be considered here. Speed required = 80/(2(2/3)) = 80/(8/3) = 80*3/8 = 30 mph. This is doable. Sufficient. So, both (A) and (B) are independently sufficient. Answer: (D)

patodrums89 · Answer

Agreed with GMAT Insight.

The Questions ask if the train WILL ARRIVE ON TIME, so is a must be true question, hence we will need some speed constraints to know if the train will cover certain distance in the given time.

If we had the average speed or a minimum allowable speed in the question stem, the answer would be C. Since we do not have it, answer is (E).

Cheers!

GMATinsight · Answer

Post For those who struggle for High order of accuracy in Data Sufficiency Hi ske I don't agree to the highlighted reasoning that you have given for statement 2, to prove the statement-2 'Insufficient'. In case, the required Speed to travel the remaining Distance, to be on time at destination, had gone above 60 mph then the statement 2 would have been sufficient to answer the question in form of 'NO' 'Train will NOT arrive on Time'. Therefore, to answer such questions we , sometimes, don't require exact speed. :-)

We can say the statement as "Not SUFFICIENT" only when the statement gives us an Inconsistent answer of the question asked in question stem. I hope this helps!

Mo2men · Answer

Is Statement 1 suff as we deduce that train will arrive on time even with delay ? or do I miss something?

GMATinsight · Answer

Statement 1 is Not sufficient because train May or May NOT reach on time depending on at what speed it travels for the rest of the journey.

The statement defines the reasoning that train has potential to reach on time but rest the question is  NOT  " Can  train reach on time?" the question is " Will  the train arrive on time?" i.e. we need to answer with certainty which we lack even after combine the two statements.

I hope this helps

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and independent equations ensures a solution.

A train runs over a straight route from town A to town D. It is scheduled to depart town A at 7am and arrive at town D at 2pm, with 10 minute stops in towns B and C. The train’s top speed is 60mph. The entire length of the route is 320 miles. Will the train arrive on time?

(1) The train experiences a 30 minute delay in town B in addition to its scheduled stop.

(2) The train travels at its top speed for exactly 75% of the trip.

From the original condition, we do not know the velocity and the distance from A to B, B to C and C to D, therefore there are 6 variables. Since we only have 1 equation (Distance from A to D which is 320), we need 5 more equations and there is only 1 each in 1) and 2) therefore we need 3 more equations. E has high probability of being the answer, and it turns out that E actually is. 
 
 Normally for cases where we need 3 more equation, such as original conditions with 3 variable, or 4 variables and 1 equation, or 5 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore E has a high chance of being the answer (especially about 90% of 2by2 questions where there are more than 3 variables), which is why we attempt to solve the question using 1) and 2) together. Here, there is 80% chance that E is the answer, while C has 15% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer according to DS definition, we solve the question assuming E would be our answer hence using ) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

Bunuel · Answer

GROCKIT OFFICIAL SOLUTION:

This is a yes/no data sufficiency. In order to answer yes or no, we need to know the time it takes the train to make its journey. From the question, we can see that the train is  supposed  to take 7 hours to go from Town A to Town D with two 10-minute stops. Thus, the total travel-time of the train is 7 hours – 20 minutes = 6 hours, 40 minutes, or 6.67 hours. A train that takes the full 6.67 hours to travel 320 miles would need to travel at a speed of approx 48mph or faster to make its timetable. Remember that this is what the train is supposed to do. Let’s see how each statement affects the time-table.

With a 30 minute delay, the train’s travel-time is now 6 hours, 10 minutes, or 6.167 hours. With that delay, the train needs to travel at approx 51mph to make its timetable. However, what is missing from this statement is proof that the train actually did increase its speed to make its timetable. Just because it was possible the train arrived on time, doesn’t mean it did. Statement (1) is insufficient.

Let’s look at  Statement (2) . 75% of the trip is 240 miles out of the total 320 miles. This means the train has to travel the remaining 80 miles in a little less than 3 hours, an average speed of approximately 25 miles an hour in order to make the timetable. This is clearly within the train’s limits, but we do not know anything about the train’s speed for these remaining 80 miles. Statement (2) is insufficient.

Combining the two statements , we know that the train only has 2 hours and 10 minutes to travel the remaining 80 miles. This requires traveling almost 40 mph. This is possible, but we have no certainty that the train accomplished this.  The answer, therefore, is (E).

KrishnakumarKA1 · Answer

Solution:

Given:  The total distance from town A to town D = 320 miles
Total time taken (7 am to 2 pm) = 7 ×60=420 mins
Maximum speed = 60 mph
Stoppage time (in town B and town C) = 10 + 10 = 20 mins
 To find:  Will train reach town D at 4 PM?

Analysis of statement 1: The train experiences a 30-minute delay in town B in addition to its scheduled stop. 
In this statement they have given there is an additional delay of 30 mins, as we do not know what is the average speed of the train we cannot find whether the train arrived on time to town D or not! (Top speed is mentioned to be 60 mph but not necessarily that train will be travelling at the top speed all the time).
So statement 1 is insufficient to answer. We can eliminate options A and D.

Analysis of statement 2: The train travels at its top speed for exactly 75% of the trip. 
Being at the top speed for exactly 75% of the trip doesn’t mean the train will arrive town D at exact time! Because we do not know what is the speed of the train for the rest 25% of the journey. We need to know the average speed of the train to find the answer. Hence statement 2 is insufficient to answer. We can eliminate option B.

Combining the statements 1 & 2: We get: 
Even after combining we cannot comment anything about the average speed of the train. Hence it is insufficient.

The correct answer option is “E”.

aronbhati · Answer

Hi Sir,

but as per question, you solved that minimum speed is 48 MPH then for option C, minimum speed is coming around 30 MPH which is lower than 48 mph so it can be answer C. please correct me where i was wrong

Gmat860sanskar · Answer

Hello Aron,

In GMAT Data insight section, most important skill is to keep track of the question stimulus and solve it accordingly. Here the main question is :
 Will the train arrive on time?

So as we can figure out remaining travel time and distance is 160 min and 80 miles respectively, so here there can be multiple cases :

Case 1: Speed in the remaining time is above 30 miles/hr then yes, we can say that it will arrive on time, However this information is not given explicitly, so we can make another case

Case 2 : Speed in remaining time is below 30 miles/hr then our answer will be No.

So here we are getting both the answer Yes and No. Clearly both statement combined is not enough.

That's why our answer here is E.

A train runs over a straight route from town A to town D. It is schedu

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