Rachel drove at a constant speed from inn A along a highway to inn B. Did Rachel reach inn B from inn A in less than an hour?
(1) If Rachel had driven to inn C that was 15 kilometers further down the highway, she would have taken 50% more time
(2) If Rachel’s average speed for the drive had been 20 kilometers per hour lesser, she would have taken 50% more time
Step 1 & 2: Understand Question and Draw Inference
Let distance between Inns A and B = D kilometers (km in short)
Let Rachel’s average speed = S kilometers per hour (kmph in short)
So, Time taken by Rachel to travel from A to B = D/S hours.
To Find: Is D/S < 1 ?
To answer the question, we need to know the value of ratio D/S
Step 3 : Analyze Statement 1 independent
Statement 1 says that: 'If Rachel had driven to inn C that was 15 kilometers further down the highway, she would have taken 50% more time’
So, not sufficient.
Step 4 : Analyze Statement 2 independent
Statement 2 says that: ‘If Rachel’s average speed for the drive had been 20 kilometers per hour lesser, she would have taken 50% more time’
Step 5: Analyze Both Statements Together (if needed)
From Statement 1: D = 30 km
From Statement 2: S = 60 kmph
Sufficient to find a unique value of the ratio D/S
Answer: Option C
Had Frank driven at an averagespeed of 40 miles per hour, he would have reached his office 10 minutes earlier than he usually
did. At what average speed should Frank drive to reach his office 20 minutes earlier than he usually did?
(1) Frank usually takes 5/6 hours to reach his office
(2) The distance to his office is 80/3 miles
Step 1 & 2: Understand Question and Draw Inference
Given:
To Find: Speed of Frank so that he takes ( ) hours to reach his office
Step 3 : Analyze Statement 1 independent
Statement1: Frank usually takes 5/6 hours to reach his office
Statement1 is sufficient to answer the question
Step 4 : Analyze Statement 2 independent
Statement2: The distance to his office is 80/3 miles
Statement2 is sufficient to answer the question.
Step 5: Analyze Both Statements Together (if needed)
As we have unique answer from steps 3 and 4 above, this step is not required.
Answer: D
John leaves from his home at 10 AM and starts driving towards a city that is 300 kilometres away, at a constant speed of 50 miles
per hour. His brother Martin leaves the home at 11:30 AM and starts driving on the same route at a constant speed of 60 miles
per hour. If they stop driving once they reach the city, which of the following statements must be true? (1 mile = 1.6 kilometres)
I. John reaches the city before Martin
II. At 1:30 PM, John is 55 kilometres ahead of Martin
III. Martin overtake John at 4 PM
Given:
To Find: Which of the 3 statements must be true?
Approach:
1. We will evaluate the 3 statements one by one
Working out:
Looking at the answer choices, we see that the correct answer is Option A
Raymond travelled from city A to city C via city B. Was his average speed for the journey from city A to city B greater than his average speed for the journey from city B to city C?
(1) Raymond’s average speed of the journey from city A to city B was greater than his average speed of the journey from city A to city C.
(2) Had Raymond travelled at a constant speed from city A to city C, the time taken by him to travel from city A to city B would have been lesser than the time taken by him to travel from city B to city C.
Step 1 & 2: Understand Question and Draw Inference
Step 3 : Analyze Statement 1 independent
(1) Raymond’s average speed of the journey from city A to city B was greater than his average speed of the journey from city A to city C.
As the denominators of the inequalities are positive, we can multiply and solve it to get
Sufficient to answer.
Step 4 : Analyze Statement 2 independent
(2) Had Raymond travelled at a constant speed from city A to city C, the time taken by him to travel from city A to city B would have been lesser than the time taken by him to travel from city B to city C.
Let Raymond’s constant speed be S kilometeres per hour
It does not tell us anything about the average speeds of Raymomd from city A to city B and city B to city C. Insufficient to answer
Step 5: Analyze Both Statements Together (if needed)
Since, we have a unique answer from step 3, this step is not required.
Answer: A
Two siblings Mark and Steve start from the same point and walk in the same direction at speeds of 5 kilometres per hour and 10 kilometres per hour respectively. After walking for an hour, Mark turns around and walks back along the same path to the starting point. Mark rests for half an hour at the starting point, and then hires a taxi driving at 30 kilometres per hour to catch up with Steve. If the taxi charges $10 for the first 2 kilometres and $2 for every subsequent 500 metres, how much in dollars does Mark pay for the taxi ride?
Given:
To Find: Amount that Mark paid to the taxi driver?
Approach:
Working out:
Answer : D
Robert and Timothy both left their respective homes at 1 PM. Robert walked till a lake that was between 2.5 kilometres and 3 kilometres from his home, inclusive, and returned home between 1:55 PM and 2:05 PM. If Timothy walked 5 kilometres more than Robert and returned to her home at 3 PM, which of the following statements must be true?
I. The walking speed of Timothy was greater than that of Robert
II. Robert’s walking speed was close to 3 kilometers per hour
III. Had Robert covered 5 more meters every 18 seconds, his walking speed would have been greater than Timothy’s
Given:
To Find:
Let Robert’s speed be SR and Timothy’s speed be ST
ST > SR?
SR ∼ 3 kmph?
meters per second (in short mps) > ST ?
Approach:
Working out:
Thus, only St. III is a must be true statement.
Correct Answer = Option C
Brian drives a certain part of his journey at an average speed of 30 miles per hour and the rest at an average speed of 60 miles per hour. If he drives for 100 miles, is his average speed for the journey greater than 45 miles per hour?
(1) Brian drives for 30 miles per hour for twice the time than he drives for 60 miles per hour.
(2) Had Brian driven at an average speed of 40 miles per hour rather than 30 miles per hour, his average speed for the
journey would have been 48 miles per hour.
Step 1 & 2: Understand Question and Draw Inference
Step 3 : Analyze Statement 1 independent
(1) Brian drives for 30 miles per hour for twice the time than he drives for 60 miles per hour.
As we know the values of x, we can find if
Sufficient to answer
Step 4 : Analyze Statement 2 independent
(2) Had Brian driven at an average speed of 40 miles per hour rather than 30 miles per hour, his average speed for the journey would have been 48 miles per hour.
As we know the values of x, we can find if
Sufficient to answer.
Step 5: Analyze Both Statements Together (if needed)
Since, we have a unique answers from steps 3 and 4, this step is not needed.
Answer: D
An international flight takes off from New Delhi in India for Washington DC in the United States of America via Doha, where the flight stops for 2 hours and 40 minutes. During flight, the average speed of the plane is 660 kilometres per hour and the flight reaches Washington DC, at 3:50 PM, Washington time. If the distance between New Delhi and Washington DC via Doha is 12000 kilometres and New Delhi is 9 hour 30 minutes ahead of Washington DC, what is the approximate time in New Delhi when the flight takes off from there?
Given:
To Find:
Delhi time at takeoff
Approach:
Delhi time at take – off = Delhi time at arrival in DC – Total journey time
of the plane
Delhi time at arrival in DC = DC Time at arrival in DC + 9.5 hours
Total journey time of the plane = Flying Time + Stopover time at Doha
Working out:
Delhi Time at arrival in DC = 3:50 PM + 9.5 hours = 1:20 AM
Flying Time :
= 1:20 AM – (24 hours – 3 hours 9 min)
= (1:20 AM – 24 hours) + 3 hour 9 min
= 1:20 AM + 3 hours 9 min
= 4:29 AM
Since this is the closest to 4:30 AM, the correct answer is Option B.
On a trip of 60 kilometres, Rita covered the first 15 kilometres at an average speed of 75 kilometres per hour and the following 35 kilometres at an average speed of 140 kilometres per hour. At what average speed did she cover the last part of her trip if her average speed for the whole trip was 80 kilometres per hour?
Given:
To Find: Average Speed for The Last Part of Trip
Approach:
2. So, to answer the question, we need to find Time Taken for Last Part of Trip:
Working out:
Looking at the answer choices, we see that the correct answer is Option D
A boat travels from Point A to Point B in the direction of water and then returns to Point A. In still water, the boat travels at a
speed of 28 kilometres per hour. If the speed of the water current is 4 kilometres per hour and the time taken for the roundtrip is 2
hours and 55 minutes, what is the total distance travelled by the boat in the round trip?
At 11 AM, Abraham leaves from his home for a meeting that is scheduled for 1 PM. If the venue of the meeting is not less than 100 kilometers away and Abraham drives at a speed not less than 60 kilometers per hour, will he be late for the meeting?
(1) The venue of the meeting is less than 120 kilometers away
(2) He does not drive at a speed greater than 80 kilometers per hour
A marathon runner starts the 26 mile run at 7.30 AM and reaches the finish line at 9.45 AM. If he runs at a constant speed throughout the marathon and water stations are put up along the route of the marathon after every 500 metres, which of the following is the closest to the time taken by the runner to go from one water station to the next one? (1 mile = 1.6 kilometres)
Megan and David start running along the perimeter of a square park. To make one round of the park, Megan takes 1 minute and
David takes 1 minute and 36 seconds. If both Megan and David burn 24 calories in making one round of the park, in how much
time will Megan have burnt 120 calories more than David?
Two trains start from City A and travel towards City B, which is at a distance of 100 miles from City A, at the same time with an
average speeds of 60 miles per hour and 80 miles per hour respectively. A train starts from City B at the same time and travels towards City A at an average speed of 70 miles per hour. How far from city B is the slower train starting from City A when the faster train starting from City A meets the train starting from City B?
The table above shows the minimum and the maximum running speeds of two animals. If Animal A runs between two poles that
are placed 20 metres apart in 3 seconds and Animal B runs between the same poles in 4 seconds, which of the following
cannot be the value of X?
I. 23
II. 26
III. 27
Patrick takes 2 hours to drive in his car from point A to point B. What is the distance between A and B?
(1) If his average speed for the journey had been 20 kilometers per hour greater, he would have taken only 1 hour and 36 minutes to reach point B
(2) Patrick covered an average of 800 meters every 36 seconds
James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James exactly 90 minutes after Patrick started his journey and then continued driving at the same speed for another 2 hours. By what percentage should Patrick reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James?
Alex and Hales started rowing towards one another at constant speeds and met after rowing for an hour. The initial distance between Alex and Hales was 20 kilometers and Alex rowed downstream while Hales rowed upstream during this journey. On some other day, the time taken by Alex alone, rowing at the same constant speed, to cover the distance between these two points going upstream was 75 minutes more than the time taken by him to cover the same distance going downstream. What was the time taken in hours by Hales to cover 20 kilometers going upstream? Assume the speed of the stream to be 4 kilometers per hour
On a Monday, John left from his home for his office at 09:05 AM and reached his office at 10:00 AM. On Tuesday, he left from his home for his office 15 minutes later than the time he left his home on Monday and reached his office 4 minutes later than the time he reached his office on Monday. If on Tuesday, John drove at an average speed that was 15 kilometres per hour faster than his average speed on Monday, how far in kilometres was his office from his home?
A man starts rowing from Point A in the direction of the water flow at a constant speed of 10 kilometers per hour. After rowing for 10 kilometers, he remembers that he forgot an important object at Point A and turns back to get it. After getting the object, he starts moving again in the direction of water flow, but due to an onset of exhaustion, he now rows at a constant speed of 8 kilometers per hour. After rowing for 26 kilometers, he reaches Point D, where he rests for 1 hour, and then resumes his journey in the same direction, rowing at a constant speed of 9 kilometers per hour, till he reaches Point B, which is 14 kilometers downstream from Point D. If the speed of water flow is 5 kilometers per hour, what is the average speed of the man for the entire journey?
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