Test: Distance/Rate Problems - GMAT MCQ

Statement (1): The length of the return trip is 24% of the entire distance traveled.
This statement alone is not sufficient to determine the average speed. While it tells us the proportion of the return trip distance to the total distance, it doesn't provide the actual distance or any information about the speed for the initial trip.

Statement (2): The length of the return trip is 100 miles.
This statement alone is not sufficient either. It gives us the distance of the return trip, but we still don't have information about the distance of the initial trip or the speed for the initial trip.

Therefore, neither statement alone is sufficient to answer the question. Considering both statements together also doesn't provide enough information to calculate the average speed. We need additional data about the distance of the initial trip to determine Aaron's average speed. The correct answer is (E): Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Statement (1) provides the information about Amy's speed during different time intervals. She traveled the first 30 minutes at 60 miles per hour and the remaining time at 80 miles per hour. However, it doesn't provide the total distance or the duration of each interval. Without the duration of each interval, we cannot determine the total distance traveled or the average speed. Therefore, statement (1) alone is not sufficient to answer the question.

Statement (2) provides the total distance between Amy and her aunt's home, which is 90 miles. With this information alone, we cannot determine the time taken or the average speed because we don't know the duration of the trip. Therefore, statement (2) alone is not sufficient to answer the question.

However, if we consider both statements together, we can derive the required information. Statement (1) gives us the speeds during different time intervals, and statement (2) gives us the total distance. By combining this information, we can calculate the duration of each interval and then find the average speed.

Hence, both statements (1) and (2) together are sufficient to answer the question. Therefore, the correct answer is (C) "BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient."

Given:
In this question, we are given

• In an endurance race, a car drove the whole race at a constant speed of 3 miles per minute to cover the total race distance D.

To find:
We need to determine

• Whether the value of D greater than 500 miles or not.

Approach and Working:

• Speed of the car = 3 miles per minute = (3 x 60) miles per hour = 180 miles per hour

As we already know the constant speed of the car is 180 miles per hour, to determine whether D was more than 500 miles or not, we need to know the time duration for which the car was driven.

Analysing Statement 1
As per the information given in statement 1, the car took more than 2 hours to complete the race.
From this statement, we can say that

• The car drove more than (180 x 2) = 360 miles in the race.
   However, we cannot say whether the distance the car was driven was more than 500 miles or not.

Hence, statement 1 is not sufficient to answer the question.

Analysing Statement 2
As per the information given in statement 2, the car took less than 2.75 hours to complete the race.
From this statement, we can say that

• The car drove less than (180 x 2.75) = 495 miles in the race.
  Therefore, we can definitely say that the distance the car was driven was not more than 500 miles.

Hence, statement 2 is sufficient to answer the question.
Hence, the correct answer is option B.

Given:

• Bob ran a 20-mile race.

To find:

• The time at which he finished the race.

Analysing Statement 1
As per the information given in statement 1, Bob started the race at 8:05 am and his average speed for the first 10 miles of the race was 8 miles per hour.

• However, we don’t have any information about Bob’s average speed for the last 10 miles.

Hence, statement 1 is not sufficient to answer the question.
Analysing Statement 2
As per the information given in statement 2, Bob ran at a constant rate and had completed half of the amount of running time at 9:20 AM and had completed 80% of the running time at 10:05 AM.

• So, he completed 30% of the distance in 45 minutes.

As he was running at a constant rate, we can say that

• He completed 50% distance in 75 minutes = 1 hour 15 minutes
  And he completed 100% distance in 150 minutes = 2 hours 30 minutes

Therefore, Bob’s starting time = (9: 20 am – 1hour 15 minutes) = 8: 05 am
And Bob’s finishing time = (8: 05 am + 2 hours 30 minutes) = 10: 35 am

Hence, statement 2 is sufficient to answer the question.
Hence, the correct answer is option B.

Statement (1) provides information about the position of Samson's Train at two different times: 9:00 a.m. and 4:00 p.m. We know that at 9:00 a.m., the train was 200 miles north of the Chasm Bridge, and at 4:00 p.m., it was 140 miles south of the bridge. However, we don't have any information about the speed of the train or its direction. Therefore, statement (1) alone is not sufficient to determine if the train was on the Chasm Bridge at 2:00 p.m.

Statement (2) gives the starting time of the trip and mentions that the train traveled at a rate of less than 70 miles per hour. However, there is no information about the position of the train at any specific time or its direction of travel. Therefore, statement (2) alone is not sufficient to determine if the train was on the Chasm Bridge at 2:00 p.m.

When we combine the information from both statements, we still don't have any additional details about the position of the train at 2:00 p.m. Therefore, statements (1) and (2) together are not sufficient to answer the question.

In conclusion, the answer is (E): Statements (1) and (2) together are not sufficient to answer the question asked, and additional data are needed.

Average speed = Total distance/Total time ;
Total distance = Avg speed * Total time

Marta averaged x miles per hour for 2 hours = 2x
y miles per hour for the remaining 3 hours = 3y
Total distance = 2x+3y

Total time = 2+3 = 5 hrs

Avg speed = 2x+3y/5

Statement 1: 2x+3y=280

Avg speed = 280/5 = 56m/h. Sufficient.

Statement 2: y = x + 10, Not sufficient.

Statement One Alone:
⇒Tom is traveling at 70 miles per hour and Samuel is traveling at 60 miles per hour.
Thus, the distance between Tom and Samuel is increasing at a rate of 70 - 60 = 10 miles per hour. If the distance increases by 10 miles each hour, then the distance between the two drivers will increase by 1 mile in 1/10 × 60 minutes = 6 minutes. So, Tom will be 3 miles ahead of Samuel in 6 minutes. Statement one is sufficient.
Eliminate answer choices B, C, and E.

Statement Two Alone:
⇒ Tom left 5 minutes before Samuel.
Without knowing anything about the speeds of each driver or the difference between the speeds of the two drivers, we cannot determine the number of minutes for Tom to increase the distance to 3 miles. For instance, if Tom travels at 70 mph and Samuel travels at 60 mph, then Tom will be 3 miles ahead of Samuel in 6 minutes, as we calculated earlier. On the other hand, if Tom travels at 80 mph and Samuel travels at 60 mph, then the distance between the two drivers will increase by 80 - 60 = 20 miles per hour. Thus, Tom will be 3 miles ahead of Samuel in 1/20 × 60 minutes = 3 minutes. Since there is more than one possible answer to the question, statement two alone is not sufficient.

Statement 1 gives the information about the total distance. But there is no clue of the speed climbing the hill. Not sufficient

Statement 2 - Distance for downtrip will also be 12. We can find the time taken for covering downtrip which is 12/18 or 2/3 hr.
Time taken for uphill = 4-2/3
= 10/3
Distance = 12

Avg speed can be found out. Sufficient