Test: Distance/Rate Problems - GMAT MCQ

The problem states that Car X leaves Town A at 2 p.m. and drives towards Town B at a constant rate of m miles per hour. Car Y starts driving from Town B to Town A, 15 minutes later, at a constant rate of n miles per hour. We need to determine whether Car X will be closer to Town A or Town B when it passes Car Y.

Statement (1) tells us that Car X arrives in Town B 90 minutes after leaving Town A. This means that Car X takes a total of 90 minutes plus the initial 15 minutes to cover the distance between Town A and Town B. However, this information alone does not give us any indication of when Car Y arrives in Town A or whether Car X will be closer to Town A or Town B when it passes Car Y. Statement (1) is not sufficient to answer the question.

Statement (2) tells us that Car Y arrives in Town A at the same time Car X arrives in Town B. This implies that the total travel time for both cars is the same. However, we still don't have any information about the speeds of the cars or the distance between the towns. Therefore, statement (2) is also not sufficient to answer the question.

When we consider both statements together, we can combine the information from both statements. Car X takes a total of 90 minutes plus the initial 15 minutes to cover the distance between Town A and Town B, and Car Y arrives in Town A at the same time Car X arrives in Town B. However, we still lack crucial information about the speeds of the cars and the distance between the towns. Therefore, even when considering both statements together, we cannot determine whether Car X will be closer to Town A or Town B when it passes Car Y.

Since neither statement alone nor both statements together provide enough information to answer the question, the correct answer is (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

To analyze the given statements and determine whether the online retailer shipped more than 35 packages on Monday, let's examine each statement individually:

Statement (1): If 4 additional packages were shipped, then the retailer would have spent at least $220 on shipping on Monday.

This statement provides information about the cost of shipping. If we assume that the retailer shipped 35 packages on Monday, the cost would be $40 for the first 10 packages and $6 for each of the remaining 25 packages (35 - 10 = 25). This results in a total cost of $40 + (25 * $6) = $190. Since $190 is less than $220, it implies that the retailer shipped more than 35 packages. Therefore, statement (1) alone is sufficient to answer the question.

Statement (2): The average price of the packages shipped on Monday was $5.50.

This statement gives us information about the average price of the packages but doesn't provide any direct information about the total number of packages shipped. It's possible to have an average price of $5.50 with any number of packages, so statement (2) alone is not sufficient to answer the question.

By combining both statements, we can determine that the retailer shipped more than 35 packages according to statement (1). Since statement (1) alone is sufficient and statement (2) is not, the correct answer is (D) EACH statement ALONE is sufficient to answer the question asked.

Statement (1): John drove one hour longer than Paul but at an average race of 5 miles per hour slower than Paul.

Statement (2): Linda drove 9 hours and averaged 50 miles per hour.

From statement (1), we know that John drove one hour longer than Paul. However, we don't have any information about the distance they each drove. Additionally, we are told that John's average speed was 5 miles per hour slower than Paul's, but we don't know either John's or Paul's average speeds. Therefore, statement (1) alone is not sufficient to determine which of the three drove the longer distance.

From statement (2), we know that Linda drove for 9 hours and averaged 50 miles per hour. This gives us the distance Linda drove, which is 9 hours * 50 miles per hour = 450 miles. However, this information alone does not help us determine whether John or Paul drove a longer distance. Therefore, statement (2) alone is not sufficient.

Combining the information from both statements, we still don't have enough information to determine which of the three drove the longer distance. We have information about Linda's distance but lack information about John's and Paul's distances. Therefore, both statements together are not sufficient.

Hence, the correct answer is (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

To solve this problem, let's analyze each statement and determine if it alone is sufficient to answer the question or if both statements together are required.

Statement (1): The distance from Madras to Trivandrum is 0.30 times the distance from Calcutta to Madras.

This statement provides a ratio between the distance from Madras to Trivandrum and the distance from Calcutta to Madras. However, it does not provide any information about the time taken to travel between the two cities. Therefore, we cannot determine the average speed from Madras to Trivandrum based on this statement alone.

Statement (2): The average speed from Madras to Trivandrum was twice that of the average speed from Calcutta to Madras.

This statement gives us a direct relationship between the average speeds from Madras to Trivandrum and Calcutta to Madras. If we assume the average speed from Calcutta to Madras is x km/h, then the average speed from Madras to Trivandrum would be 2x km/h. This statement alone allows us to determine the average speed from Madras to Trivandrum.

When we combine both statements, we can use the information from statement (2) to assign variables to the average speeds. Let's assume the average speed from Calcutta to Madras is x km/h and the average speed from Madras to Trivandrum is y km/h. From statement (2), we know that y = 2x.

We also know from the question that the average speed for the entire journey (from Calcutta to Trivandrum) is 40 km/h. Therefore, we can set up the following equation:

Total distance / Total time = Average speed
(0.30x + x) / (0.30x/x + x/y) = 40

Simplifying the equation:

0.30x + x = 40(0.30 + 1/2)

0.30x + x = 40(0.30 + 0.50)

1.30x = 40(0.80)

1.30x = 32

x = 32 / 1.30

x ≈ 24.62 km/h

Now that we have determined the value of x, we can find y by substituting it back into the equation y = 2x:

y = 2(24.62)

y ≈ 49.24 km/h

Therefore, both statements together are sufficient to determine the average speed from Madras to Trivandrum, which is approximately 49.24 km/h. The answer is (C).

Statement (1) tells us that the average speed for the journey is 48 miles per hour. This implies that the total time taken for the journey is given by the equation:

Total Time = Total Distance / Average Speed

From the information given, we know that the total distance traveled is 240 miles. Plugging in the values, we have:

Total Time = 240 miles / 48 miles per hour Total Time = 5 hours

However, this information alone does not provide us with any specific details about the time spent traveling at the speed of z miles per hour. Therefore, statement (1) alone is not sufficient to answer the question.

Moving on to statement (2), it states that z is greater than 48 miles per hour. This provides us with an inequality, but it doesn't give us any specific value for z or any information about the time spent traveling at that speed. Therefore, statement (2) alone is not sufficient to answer the question.

Now, let's consider both statements together. Statement (1) tells us that the total time taken for the journey is 5 hours, and statement (2) tells us that z is greater than 48 miles per hour. However, even with this combined information, we still do not have enough data to determine how long Pat was traveling at the speed of z miles per hour. We have no information about the distribution of time between the two speeds or any relationship between x and z.

Hence, the correct answer is (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

The given problem is a Data Sufficiency question from the GMAT. Let's analyze the two statements provided and determine their individual sufficiency and their combined sufficiency.

Statement (1): Sam drove the first hour of the three-hour trip from Nurich to Greensburg at 5 miles per hour faster than he drove the final 2 hours.

This statement provides information about the speed Sam drove for the first hour compared to the speed for the final 2 hours. However, we don't have any information about the actual speeds. Without the actual speeds, we cannot determine the distance traveled or calculate the length of the route. Therefore, statement (1) alone is not sufficient to answer the question.

Statement (2): Sam drove the first 1/3 of the trip from Nurich to Greensburg at 38 miles per hour.

This statement gives us the speed at which Sam drove for the first 1/3 of the trip. However, we don't have any information about the remaining 2/3 of the trip. Without the information about the remaining distance and speeds, we cannot calculate the total distance of the route. Therefore, statement (2) alone is not sufficient to answer the question.

Combining the statements, we still don't have enough information. Statement (1) provides information about the speeds during different time periods, but no actual speeds are given. Statement (2) provides the speed for the first 1/3 of the trip, but no information about the remaining 2/3 is provided.

Since neither statement alone is sufficient to answer the question, and the combination of both statements is also insufficient, we can conclude that both statements together are sufficient to answer the question. The answer is (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.

The given question is asking whether the time required to travel a certain distance is greater when traveling at a certain speed compared to a different distance at a different speed. We need to determine if the information provided in statements (1) and (2) is sufficient to answer this question.

Statement (1): d = D + 20
This statement tells us that the distance d is 20 miles more than the distance D. However, it does not provide any information about the speeds at which the distances are traveled. Without information about the speeds, we cannot determine the relative times required for the two distances. Therefore, statement (1) alone is not sufficient to answer the question.

Statement (2): r = R + 20
This statement tells us that the speed r is 20 miles per hour more than the speed R. Similar to statement (1), this statement does not provide any information about the distances traveled. Without information about the distances, we cannot determine the relative times required for the two speeds. Therefore, statement (2) alone is not sufficient to answer the question.

Considering both statements together, we have information about the distances and speeds. However, since we still don't know the specific values for d, D, r, and R, we cannot calculate the times required to travel the distances. Therefore, statements (1) and (2) together are not sufficient to answer the question.

Since neither statement alone nor both statements together are sufficient, the correct answer is (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

To determine who among contestants B and D finished third in the 200-meter race, let's analyze the information provided in each statement:

Statement (1): A beat B by 14 seconds, and C beat D by 12 meters.
This statement gives us two pieces of information: the time difference between A and B, and the distance difference between C and D. However, we don't have a direct comparison between B and D. Without knowing the relationship between time and distance in this context, we can't determine who finished third based on this statement alone.

Statement (2): A finished the race in 25 seconds, and D finished 20 meters behind A.
This statement provides the time taken by A to complete the race and the distance difference between A and D. Again, we don't have a direct comparison between B and D. Without knowing the relationship between time and distance, we can't determine who finished third based on this statement alone.

Combining both statements:
By combining both statements, we can establish a relationship between time and distance. Statement (1) tells us that the time difference between A and B is 14 seconds, while statement (2) informs us that the distance difference between A and D is 20 meters. However, even with this information, we still cannot directly compare B and D since we don't have a direct relationship between time and distance.

Therefore, when both statements are considered together, we still cannot determine who finished third among B and D. As a result, the correct answer is (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

In summary, neither statement alone provides enough information to determine the third-place finisher, and even when both statements are combined, additional data is required to make a conclusive determination.

The given problem involves determining the distance Rebeca drives to work based on her driving speed.

Let's analyze each statement separately:

Statement (1): x and y differ by seven miles per hour.

This statement provides the difference in speeds between x and y, but it doesn't provide any specific information about their values or the relationship between them. We cannot determine the distance based on this statement alone.

Statement (2): y is 11% greater than x.

This statement gives us a specific relationship between x and y, stating that y is 11% greater than x. However, without knowing the actual values of x or y, we cannot determine the distance Rebeca drives.

Considering both statements together:

When we combine the information from both statements, we can deduce some additional information. Let's say x represents Rebeca's driving speed in miles per hour. From statement (1), we can infer that y is x + 7 mph. Furthermore, statement (2) tells us that y is 11% greater than x. Mathematically, this can be expressed as y = x + 0.11x = 1.11x.

Now, we can set up equations based on the given time differences:

Equation 1: Distance / x = Time (One minute late)
Equation 2: Distance / y = Time (One minute early)

Since the distance remains the same in both equations, we can equate them:

Distance / x = Distance / y

Cross-multiplying, we get:

Distance * y = Distance * x

Since y = 1.11x (from statement 2), we can substitute it into the equation:

Distance * 1.11x = Distance * x

Dividing both sides by Distance and canceling out the common factor of Distance, we have:

1.11x = x

Simplifying further, we get:

0.11x = 0

This equation implies that x must be 0, which doesn't make sense in the context of the problem. Therefore, this scenario is not possible.

Hence, the combination of both statements (1) and (2) together is not sufficient to determine the distance Rebeca drives to work. Therefore, the answer is (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

The given problem provides information about Sarah's round trip from point A to point B. We need to determine the time it takes for Sarah to drive from A to B.

Let's analyze each statement:

Statement (1): Total round trip distance from A to B and back is 90 miles.
This statement tells us the total distance of the round trip but does not provide any information about the individual distances from A to B or from B to A. Therefore, statement (1) alone is not sufficient to determine the time it takes for Sarah to drive from A to B.

Statement (2): Distance from B to A is 25% more than the distance from A to B because of the diversion.
This statement provides a relationship between the distances from A to B and from B to A. However, it does not give us the actual distances. Without knowing the actual distances, we cannot calculate the time it takes for Sarah to drive from A to B. Therefore, statement (2) alone is not sufficient to answer the question.

By analyzing both statements together, we still don't have enough information to calculate the time taken for Sarah to drive from A to B. While statement (1) gives us the total round trip distance and statement (2) provides a relationship between the distances, we still need the actual distances to calculate the time. Thus, both statements together are not sufficient.

Since neither statement alone nor both statements together provide enough information, the answer is (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.