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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 18 Jul 2024, 19:26
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­Answer E
Both information are insufficent
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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 18 Jul 2024, 21:24
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Bunuel
Train A and Train B each departed simultaneously from Liverpool heading to London, which is 300 kilometers away. When Train A reached the destination, Train B still had 80 kilometers left to cover. What was Train A's average speed during this journey?

(1) During the first hour, Train B covered 40 kilometers less than Train A.

(2) Train B's average speed for the first 110 kilometers was 110 kilometers per hour.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

 


This question was provided by GMAT Club
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Given the information in the stimulus, Train A covers 300km in the same time that Train B covers 300-80 = 220km.

Thus if A and B are their speeds respectively;
A:B = 300:220 = 15:11
Hence, let A = 15k and B = 11.

(1) During the first hour, Train B covered 40 kilometres less than Train A.
Thus 15k*1 - 11k*1 = 40 or k= 10, A= 15k= 150 km/h. (1) alone is sufficient to answer.

(2) Train B's average speed for the first 110 kilometers was 110 kilometers per hour.
Thus 11k= 110, or A = 15*10 = 150 km/h. (2) alone is sufficient to answer.

Each statement alone is sufficient to answer the question.

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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 18 Jul 2024, 21:28
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­What we know is that in the same time train A covered 300km, train B covered only 220.

(1)
This gives us nothing by itself. Insufficient.

(2) 
This tells us that train B covered 110 km in the first hour, which is not representative of the whole journey. Insufficient.

(1+2)
Okay, in the first hour train A covered 150km and train B covered 110. Their respective speeds were also 150 and 110.
DOes it tell us anything about the whole journey? Not really, because we don't know whether afterwards any of the trains slowed down or sped up - there's no guarantee they have the same speed. Insufficient.

The right answer is E.
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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 18 Jul 2024, 22:05
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­Let's start by summarizing the given information:


  • Train A and Train B both departed simultaneously from Liverpool to London, a distance of 300 kms.
  • When Train A reached London, Train B still had 80 kilometres left to cover.
From this, we know that when Train A had covered 300 kms, Train B had covered 300−80 = 220 kms.

Let a​ and b be the average speeds of Train A and Train B, respectively.

We need to find the average speed of Train A.

Statement (1):

During the first hour, Train B covered 40 kms less than Train A.

Let x be the distance covered by Train A in the first hour. The distance covered by Train B in the first hour = x - 40

From the above, we can say a = x and b = x-40
If we know x we can calculate a, but we don't know x. So Statement (1) is not sufficient 

Statement (2):

Train B's average speed for the first 110 kms was 110 kms per hour.

This tells us that Train B travelled the first 110 kms in: 110 km/h
This information tells us nothing about Train A's average speed for the whole 

Analyzing Statements (1) and (2) Together:

Let's combine the information:

From Statement (1): a = x and b = x-40
From Statement (2): Train B's speed for the first 110 kms is 110 km/h, meaning it took Train B 1 hour to cover this distance => 110 = x-40 => x = 150In the first hour, Train B covered 110 kms, so according to Statement (1), Train A must have covered 110+40=150 150 kms in the first hour.

Thus, the speed of Train A in the first hour is 150 km/h.

Given Train A's average speed over the entire journey was consistent, we can infer it is 150 km/h.

C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.­
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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 18 Jul 2024, 22:07
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Bunuel
Train A and Train B each departed simultaneously from Liverpool heading to London, which is 300 kilometers away. When Train A reached the destination, Train B still had 80 kilometers left to cover. What was Train A's average speed during this journey?

(1) During the first hour, Train B covered 40 kilometers less than Train A.

(2) Train B's average speed for the first 110 kilometers was 110 kilometers per hour.
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­Statement 1: 
This means that durnig the first hour, the relative speed of the two trains is 40 km/hr.
We know that by the end, the relative distance will be 80 km.
But we don't know what the speeds of the trains were during the rest of the journey. We also don't know how much distance the trains travelled in the first hour.
We have not been told that the trains are travelling at a constant speed.

e.g.
The speed of train A could be a constant 100 km/hr
Train B will need to have a speed of 60 km/hr during the first hour.
Now, for the rest of the journey, train B's speed could be 80 km/hr.
By the time train A reaches the destination, i.e in 3 hours, train B would have covered 220 km distance leaving 80 km between them which satisfies the given condition.

Another case could be that Train A travels at 150 km/hr
and Train B travels at 110 km/hr.
This case will also satisfy the given condition but the avg speed of train A is different.

Insufficient.

Statement 2:
Train B's avg speed during the first hour is 110 km/hr
This faces the same problem as before. We cannot estimate the time taken by train A to reach the destination.

Insufficient.

Both together.
Train B's avg speed during the first hour is 110 km/hr
Train A's avg speed during the first hour is 150 km/hr

Rest of the journey could be travelled at constant speeds of both trains which will give us the avg speed of train A = 150 km/hr.

It could also happen that Train A slows down and travels at 50 km/hr and train B travels at \(\frac{110}{3}\) km/hr
Train A will reach its destination in a total of 4 hrs with avg speed of \(\frac{300}{4}\) km/hr
while train B reaches the 220 km mark.

Insufficient.

E­
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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 18 Jul 2024, 22:27
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Quote:
­Train A and Train B each departed simultaneously from Liverpool heading to London, which is 300 kilometers away. When Train A reached the destination, Train B still had 80 kilometers left to cover. What was Train A's average speed during this journey?

(1) During the first hour, Train B covered 40 kilometers less than Train A.

(2) Train B's average speed for the first 110 kilometers was 110 kilometers per hour.
Show more
Sb*(300/Sa) = 220, is given as per the statement.

(1) Sb = Sa-40. This is just for the first hour, and we have been asked the average for the whole journey. Insufficient.
(2) This again gives us partial info as first. Hence, insufficient.

Taking 1 and 2 together, we just have the data for average speed of the first hour, we can't really tell what was the average speed of both the trains after the first hour as it could vary.

Hence, the answer is (E).
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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 18 Jul 2024, 22:39
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avg speed of A=va
avg speed of B=vb
t =time for Train A to reach London.

Given- vA​*t=300,  vB*t=220

Va=?

1--Db​=DA​−40 
In one hour Da=va*1

But is doesnt tell whether it will maintain the same speed during the whole journey or not 
So statement 1 not suff

2--Avg speed for the first 110 km=110 km/h
Time taken for 110 km= 1 hour

But we dont know whether this speed will be maintained or not in the whole journey so

Statement 2 not suff

1+2 No info about the speed of the train will it be constant or diff so will not be able to claculate the speed of A

Ans is E Each statment not suff


 
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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 18 Jul 2024, 23:10
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Train A and Train B each departed simultaneously from Liverpool heading to London, which is 300 kilometers away. When Train A reached the destination, Train B still had 80 kilometers left to cover. What was Train A's average speed during this journey?

We are given the distance 300kms. All we need is total time taken by A. None of these two options are useful to determine the total time taken unless we assume (which we shouldn't) A had the same speed throughout; hence E is the answer.

(1) During the first hour, Train B covered 40 kilometers less than Train A.

(2) Train B's average speed for the first 110 kilometers was 110 kilometers per hour.
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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 18 Jul 2024, 23:12
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Bunuel
Train A and Train B each departed simultaneously from Liverpool heading to London, which is 300 kilometers away. When Train A reached the destination, Train B still had 80 kilometers left to cover. What was Train A's average speed during this journey?

(1) During the first hour, Train B covered 40 kilometers less than Train A.

(2) Train B's average speed for the first 110 kilometers was 110 kilometers per hour.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

­
 ­
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­Train A:
Speed = Sa km/h,
Distance = 300km,
Time taken = t hours,

Train B:
Speed = Sb km/h,
Distance = 220km,
Time taken = t hours,

(1) During the first hour, Train B covered 40 kilometers less than Train A.
=> Da = Db + 40
=> Sa = Sb + 40
  • Here, we got the relationship between speeds of 2 trains. If Average speed was not different in next hours of journey then we can calculate the time taken by train A, which gives average speed of train A.
  • But, we don't know whether the average speed was same or not. So, we can not deduce the avg. speed.
  • Hence, we can eliminate options A, D.
(2) Train B's average speed for the first 110 kilometers was 110 kilometers per hour.
=> Sb = 110 km/h
  • If average speed for B was the same in next 1 hour(as remaining distance to be covered in time(t) is 220km) then we could have calculated time taken by train B and using that time we could have determined avg. speed of train A.
  • As, we don't know the avg. speed in next 1hr for train B. We can not get the answer.
  • Hence, we can eliminate option B.
If we combine both the statements then also we can't get the answer as we don't have any information about next hour.

\(Distance = Avg. Speed * Time taken\)

Here, depending of Avg. Speed time will vary means we can not deduce any particular answer.

Answer: E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

 
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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 18 Jul 2024, 23:17
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Required -
Train A Avg. Speed=?

Given-

Train A is faster than train B, completed 300KM, while train B covered only 220 KM

Sa*Ta=300
Sa*Tb=220

Option-1, in First 1- hour
Sa*1=Sb*1+40
Sa=Sb+40
Not sufficent alone


Option-1, Train B's average speed for the first 110 kilometers was 110 kilometers per hour.
Means for first 1 hour train speed=110 KM/Hour
Sb=110
Sa?
Not sufficent alone

Together

For, First 1-hour
Sb=110
Sa=150

Average speed of whole journey is still unknown.

Ans-E
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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 19 Jul 2024, 00:09
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Constant speed is not mentioned and it is unknown that how long did Train A spend
­St1 --  During the first hour, Train B covered 40 kilometers less than Train A.
This does not tell much, maybe they were slower during second hour, not sufficient
St2 -- Train B's average speed for the first 110 kilometers was 110 kilometers per hour.
What happened in second or third hours, not sufficient
Combined -- Still do not know long how the entire journey took, only first hour is known, maybe there is second or third hours, not sufficient
E
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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 19 Jul 2024, 00:49
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Its not given that the trains are running at a constant speed. Hence E.
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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 19 Jul 2024, 01:00
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(1) During the first hour, Train B covered 40 kilometers less than Train A.
So, after 2 hours, Train B was 80 kilometers behind Train A.
So, it took 2 hours for Train A to reach Liverpool. His average speed was 150 km/h.
This statement is sufficient. 

(2) Train B's average speed for the first 110 kilometers was 110 kilometers per hour.
Thi statement is insufficient. We don't now if the speed was constant after the first hour. 

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
 
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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 19 Jul 2024, 01:09
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Answer is C
The stem gives us relative distance but we can't find individual speed from that
Statement 1 gives relative distance in 1 hour. But this info brings in many combination of values hence not sufficient
Statement 2 gives Speed of B but we cannot find unique value of A
Taking both together we have relative distance and value of B from which we can find unique value of speed of A
Hence C
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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 19 Jul 2024, 01:30
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Train A and Train B each departed simultaneously from Liverpool heading to London, which is 300 kilometers away. When Train A reached the destination, Train B still had 80 kilometers left to cover. What was Train A's average speed during this journey?

(1) During the first hour, Train B covered 40 kilometers less than Train A.

(2) Train B's average speed for the first 110 kilometers was 110 kilometers per hour.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.­


Answer ->
D = 300
Let T1 and T2 be the time taken by Train A and Train B to reach London respectively.
Train A's average speed = ?

Statement 1 - We don't know if train B maintained the same average speed in second hour.
Not sufficient

Statement 2 - We don't know the time taken by train B to cover the distance from 110 Km to 220 Km.
Not sufficient

Both - average speed of Train A in first hour = 150 Km/hr
We don't the average speed for second hour for neither of the two trains and we can't assume that they maintained the same speed.
Not sufficient

E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.­
 
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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 19 Jul 2024, 02:10
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Let's first analyze the information given in the problem:

Train A reaches the destination (300 km) when Train B still has 80 km left.
This means Train B has covered 220 km when Train A has covered 300 km.
Let vA and vB be the average speeds of Train A and Train B, respectively.
Let t be the time it took for Train A to travel 300 km.

From the information given:
𝑣𝐴=300
𝑡vA​= t300
​𝑣𝐵=220
𝑡vB=t220
​


To find
vA we needt, the time Train A took to travel 300 km.

Statement (1): During the first hour, Train B covered 40 kilometers less than Train A.

Let's denote the distance Train A covered in the first hour as

dA and the distance Train B covered in the first hour as dB.

From statement (1):

𝑑𝐵=𝑑𝐴−40

This gives us one equation, but it does not directly provide
t or vA
​
Statement (2): Train B's average speed for the first 110 kilometers was 110 kilometers per hour.

This means Train B traveled the first 110 kilometers in 1 hour:
𝑡𝐵1=110/110=1hour

Train B still needs to cover
220−110=110 kilometers. This second part of the journey is done in t−1 hours. The average speed of Train B for the entire 220 kilometers journey is:
vB=t220
​
Since the first part of the journey took 1 hour at 110 km/h, for the second part of the journey (110 km), the speed and time relation is:
𝑣𝐵2×(𝑡−1)=110
vB2 ×(t−1)=110
​


We also have:
220/𝑡 = 110/1+ 110(𝑡−1)

By solving this equation, we can find t and subsequently 𝑣𝐴=300𝑡
Combining both statements:

With statement (1), we have a relation between the speeds of Train A and Train B during the first hour, and with statement (2), we have detailed information on Train B's speed during the initial and subsequent phases of its journey. This combined information allows us to determine the exact average speeds of both trains and thus find
t. Hence C.
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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 19 Jul 2024, 02:12
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Total DIstance D = 300km
Avg speed of A: Aav; AVg speed of B: Bav
300/Aav=220/Bav
15Bav= 11Aav----(1)
Train A's average speed during this journey / Aav = ?

(1)  During the first hour, Train B covered 40 kilometers less than Train A
      t=1
      Let b be speed of Train B in 1st hr and a for Train A in 1st hr
       x/b=(x+40)/a
      Since it is not specified that the trains travel with constant speed
      b is not equal to Bav. a is not equal to Aavg.

       Not sufficient
(2) B travels at 110km / hr for 1st hour
     Not sufficient

(1) & (2)

x/110 = (x+40)/a
110/110=150/a
a=150 km / hr for 1st hour
 Not sufficient to calculate average speed for entire journey

Ans E

Bunuel
Train A and Train B each departed simultaneously from Liverpool heading to London, which is 300 kilometers away. When Train A reached the destination, Train B still had 80 kilometers left to cover. What was Train A's average speed during this journey?

(1) During the first hour, Train B covered 40 kilometers less than Train A.

(2) Train B's average speed for the first 110 kilometers was 110 kilometers per hour.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

 


This question was provided by GMAT Club
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­
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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 19 Jul 2024, 02:17
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Bunuel
Train A and Train B each departed simultaneously from Liverpool heading to London, which is 300 kilometers away. When Train A reached the destination, Train B still had 80 kilometers left to cover. What was Train A's average speed during this journey?

(1) During the first hour, Train B covered 40 kilometers less than Train A.

(2) Train B's average speed for the first 110 kilometers was 110 kilometers per hour.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

 


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­L-------------------------------L
               300 

So train A travelled 300Km
train B travelled 220 Km in the same time

We need to find avg speed of train A: 

Let the speeds be a, b. As we know the time is same:
300/a = 220/b
(1) During the first hour, Train B covered 40 kilometers less than Train A.

This means that a-b =40. 

a = 300/220 b =>15b/11

So 4b/11 =40; b=110; a=150. 

Hence A,D can be the choices

(2) Train B's average speed for the first 110 kilometers was 110 kilometers per hour.

b =110, Avg speed is same for the overall trip. 

So time taken by A to reach destination is same as b reaching 22 mark I,e. 2hrs. 

Hence a = 150

IMO D­
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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 19 Jul 2024, 02:26
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Train A and Train B each departed simultaneously from Liverpool heading to London, which is 300 kilometers away. When Train A reached the destination, Train B still had 80 kilometers left to cover. What was Train A's average speed during this journey?

Let average speed of Train A and Train B be x km/hr and y km/hr 

At t=0 

Liverpool    Train A_(x km/hr)____________________300 Km_______________________________________________    London
                Train B (y km/hr)                                               

At t=t'

Liverpool    ____________________________________________________________________________________Train A    London
                                                                  220 Km                                                  Train B       80 kms

At t=t',
t(A)=t(B)= distance travelled/avg speed
300 /x = 220 /y 
30/x=22/y
x=15y/11...............................................................(i)


(1) During the first hour, Train B covered 40 kilometers less than Train A.


At t=1 hr

Liverpool    ________________________x kms__________________Train A______________________________________    London
                                                      Train B <----40 kms---------->                                                               

x /x = (x-40) /y =1
x-40=y........................................................................(ii)

 From (i), x=15y/11
x=15(x-40)/11
11x=15x-600
4x=600
x=150 km/hr
Sufficient.

(2) Train B's average speed for the first 110 kilometers was 110 kilometers per hour.

At t=T

Liverpool    _______________________________________________Train A________________________________________    London
                 <---------------------------110 kms---------------->Train B  (y=110 kmph)                                             

 ­Avg speed=distance travelled/time taken
110=110/T
t=T=1 hour

 From (i)
x=15(110)/11
=150 km/hr
Sufficient.


Ans. D­
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GMAT Club Olympics 2024 (Day 9): Train A and Train B each departed 19 Jul 2024, 02:29
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Bunuel
Train A and Train B each departed simultaneously from Liverpool heading to London, which is 300 kilometers away. When Train A reached the destination, Train B still had 80 kilometers left to cover. What was Train A's average speed during this journey?

(1) During the first hour, Train B covered 40 kilometers less than Train A.

(2) Train B's average speed for the first 110 kilometers was 110 kilometers per hour.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

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