Test: Distance And Speed- 2 - GMAT MCQ

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

Step 1 & 2: Understand Question and Draw Inference

Given:

• Let Frank’s usual time to reach his office be t hours
• So, when speed of Frank = 40 miles per hour, he takes () hours to reach his office
• Distance to Frank’s office = 40 * () miles

To Find: Speed of Frank so that he takes ( ) hours to reach his office

• Let the speed of Frank be S miles per hour
• Hence, Distance covered by Frank driving at S miles per hour for() hours = S*()miles
• Now, we know that distance to Frank’s office = 40 * () miles
• So,we can write   S*() =  40 * ()
  • Hence, to find the value of S, we need to find the value of t.

 Step 3 : Analyze Statement 1 independent

Statement-1: Frank usually takes 5/6  hours to reach his office

• We are given that t = 5/6 hours. So, we can find the value of S

Statement-1 is sufficient to answer the question

Step 4 : Analyze Statement 2 independent

Statement-2: The distance to his office is 80/3 miles

• We know that disatance to Frank’s office is 40 * ()
• So, we can write 40 * () = 80/3 miles .
  • As it is a linear equation in t, we can find the value of t
• Once we know the value of t. we can find the value of S

Statement-2 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

Given:

• Home – City distance = 300 km
• John:
  • Speed = 50 miles per hour (Note that the distance is given in kilometers and John’s speed is given in miles per hour)
    • 1 mile = 1.6 kilometers
  • Time of start= 10 AM
• Martin:
  • Speed = 60 miles per hour
  • Time of start = 11:30 AM

To Find: Which of the 3 statements must be true?

Approach:

1. We will evaluate the 3 statements one by one

Working out:

• Evaluating Statement I
  • To evaluate this statement, we need to find the time at which John reaches the city and the time at which Martin reaches the city
  • John:
    • Speed = 50 miles per hour = 50*1.6 kilometers per hour
    • So, time (hours) =
    • John starts at 10 AM
    • So, John reaches the city at 10 AM + 3 hours 45 min = 1:45 PM
  • Martin:
    • Speed = 60 miles per hour = 60*1.6 kilometers per hour
    • So, time (hours) =
    • Martin starts at 11:30 AM
    • So, Martin reaches the city at 11:30 AM + 3 hours 7.5 min = 2: (37.5) PM
  • Therefore, Statement I is indeed true
• Evaluating Statement II
  • At 1:30 PM, John has been travelling for (1:30 PM – 10 AM =) 3.5 hours and Martin for (1:30 PM – 11:30 AM =) 2 hours

• So, distance between them at 1:30 PM = 280 – 192 = 88 km
• Therefore, Statement II is not true

• Evaluating Statement III
  • In our analysis of Statement I, we’ve already seen that John reached the city before Martin. Since both of them stop driving once they reach the city, Martin never manages to overtake John (and none of them are still driving at 4 PM)
  • Therefore, Statement III is not true.
• Getting to the answer
  • Thus, we see that out of the 3 statements, only Statement I is true.

Looking at the answer choices, we see that the correct answer is Option A

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

Given:

• Speed of Mark = 5 kilometres per hour
• Speed of Steve = 10 kilometres per hour
• Time after which Mark turns around and walks back = 1 hour
• Time for which Mark rests = 0.5 hour
• Speed of taxi = 30 kilometres per hour
  • Charges for the first 2 kilometres = $10
  • Chrages for every subsequent 500 metres = $2

To Find: Amount that Mark paid to the taxi driver?

Approach:

1. For finding the amount that Mark paid to the taxi driver, we need to find the distance travelled by the taxi.
2. As the taxi started from the starting point of Steve and stopped when it caught up with Steve, the (Distance travelled by the taxi) = (Distance travelled by Steve since he started walking)
3. Distance travelled by Steve = Speed of Steve * Time taken
   • We are given that speed of steve = 10 kilometres per hour. We need to find the time for which Steve travelled
4. The travelling time of Steve can be divided into 4 phases:
   1. Phase-I: Time for which Mark and Steve both walked = 1 hour
   2. Phase-II: Time taken by Mark to reach back the starting point = 1hour
      • As Mark travelled one way for 1 hour and travelled back the same path at the same speed, he will take the same time
      • Please note that Steve kept walking ahead during this time
   3. Phase-III: Time for which Mark rests = 0.5 hour
      • Plesae note that Steve kept walking ahead during this time
   4. Phase-IV: Time for which the taxi drove = t hours
      1. For this phase, the distance travelled by taxi = total distance travelled by Steve
      2. The time for which the taxi would travel would be equal to the time for which Steve would be travelling in this phase.
      3. As we know the speeds of both taxi and Steve, we can formulate an equation by equating the time taken.
   5. We will find the distance travelled by Steve in each of the phases and then sum it up to get the total distance distance travelled by Steve

Working out:

1. Phase-I: Distance travelled by Steve = 10 * 1 = 10 kilometres
2. Phase-II: Distance travelled by Steve = 10 * 1 = 10 kilomtres
3. Phase-III: Disatnce travelled by Steve = 10 * 0.5 = 5 kilomtres
4. Phase-IV:
   • Let the distance covered by Steve in time t hours be x kilometres. 
   • Total distance covered by taxi to catch up with Steve = 10 + 10 + 5 + x = 25 + x kilometres
     • Time taken by taxi to cover 25 + x kilometres, i.e. t = 
   • We can equate the time taken by taxi and Steve
     • ​
5. So, total distance travelled by the taxi = 25 + 12.5 = 37.5 kilomtres
6. Charges for the first 2 kilometres = $10
7. Charges for the rest 35.5 kilomtres = 35.5 * 2 * 2 = $142
8. Hence, total amount paid to the taxi driver = $10 + $ 142 = $152.

Answer : D 

Given:

• Robert
  • Let the distance covered be DR and time taken be TR
  • 2.5*2 km ≤ DR ≤ 3*2 (distance in round trip is double the one-way distance)

• Timothy
  • Let the distance covered be DT and time taken be TT
  • As Timothy walked 5 kilometers more than Robert, she would have walked a minimum distance of 5 + 5 = 10 kms and a maximum distance of 6 + 5 = 11 kms.
  • So, 10 km ≤ DT ≤ 11
  • TT = 2 hours

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:

• Find range of SR and ST (since definite values of DR, TR and TT are not given, definite values of SR and ST cannot be found)

• Check the validity of the 3 statements

Working out:

• Range of ST

• SR + 1 kmph: 5.6 kmph – 7.7 kmph
• Thus, Robert’s speed would definitely have been greater than
• Timothy’s
• So, Yes

Thus, only St. III is a must be true statement.
Correct Answer = Option C

Step 1 & 2: Understand Question and Draw Inference

• Let the distance for which he drives for 30 miles per hour be x miles.
• Distance for which he drives for 60 miles per hour = 100 – x miles
• 

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

Given:

• Delhi -> Doha (2 hr 40 min stop) -> DC
  • Average flying speed = 660 kmph
    • Flying distance = 12000 km
• DC Time at Arrival in DC = 3:50 PM
• Delhi Time – DC Time = 9.5 hours

To Find:

Delhi time at take-off

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 :

• Total Journey time of the plane = 18 hours 11 minutes + 2 hours 40 minutes = 20 hours 51 minutes
• So, Delhi time at take – off = 1:20 AM – 20 hours 51 minutes

= 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.

Given:

• The Whole Trip:
  • Total distance = 60 km
  • The Average Speed for the whole trip = 80 kmph
• Part 1 of Trip:
  • Distance = 15 km
  • Average Speed = 75 kmph
• Part 2 of Trip:
  • Distance = 35 km
  • Average Speed = 140 kmph
• The Last Part of Trip:
  • Distance = 60 – (15 + 35) = 60 – 50 = 10 km

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:

• Finding Time taken for Last Part of Trip:

Looking at the answer choices, we see that the correct answer is Option D