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GMAT Club Olympics 2024 (Day 4): What is the length of a train

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FranCifu

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11 Jul 2024, 18:33

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We are given the speed, so for sufficiency we need the time, and the relation between distance of bridge and the length of the train.

From the stimulus we have the speed and time it takes to cross A, so the distance is Speed * Time = 90*10 = 900.

St 1 --> Sufficient: it gives the relation between distance and lenght, and we know the distance.
St 2 --> Insufficient: we get the speed of crossing B, but it says nothing about relation with length.

Answer is A

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x = length of the train
y = length of the bridge A

We know that:

(x + y)/10 = 90
x + y = 900

We want to know x.

(1)
y = 5x

x + 5x = 900
6x = 900
x = 150

SUFFICIENT

(2)
(x + 4y)/35 = 90
x + 4y = 3150

Solving with x + y = 900
3y = 2250
y = 750
x = 150

SUFFICIENT

IMO D

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Bunuel

What is the length of a train traveling at a constant speed of 90 meters per second, if it crosses Bridge A in 10 seconds, from the moment it enters the bridge to the moment its last carriage exits the bridge?

(1) The length of Bridge A is five times the length of the train.
(2) During the journey, the train crosses Bridge B, which is four times the length of Bridge A, in 35 seconds.

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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Total distance = len of bridge A + len of train -> 90*10 = 900m

(1) The length of Bridge A is five times the length of the train.
len bridge A = 5*len train, substituting in above equation for len train - Sufficient

(2) During the journey, the train crosses Bridge B, which is four times the length of Bridge A, in 35 seconds.
len bridge B = 4 len bridge A
len bridge B + len train = 35*90 = 3150 -> can substitute with len bridge A and along with first equation from stem - sufficient

Answer (D)

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11 Jul 2024, 19:25

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Both options will result in different answers, hence E.

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11 Jul 2024, 20:07

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Speed of Train = 90 m/s
Let the length of the train be L
Time to cross bridge A = 10s

Let's analyze the statements:

(1) The length of Bridge A is five times the length of the train.

Length of bridge A = 5L
Total distance covered by the train while crossing bridge A = 5L + L = 6L
Or, 90 m/s * 10 s = 900 m
6L = 900
L = 150 m

(2) During the journey, the train crosses Bridge B, which is four times the length of Bridge A, in 35 seconds.

Length of bridge B = 4*5L = 20L
Total distance covered by the train while crossing bridge B = 20L + L = 21L
Or, 90 m/s * 35 s = 3150 m
21L = 3150
L = 150 m

Since both the statements independently give conclusive results.

Correct Option: D

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Bunuel

This question was provided by GMAT Club
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Speed of train (S) = 90 m/s
It crosses Bridge A in 10s, according to given information (from the moment it enters the bridge to the moment its last carriage exits the bridge), total length = La + Lt

La + Lt = 90*10 = 900

1) La = 5*Lt, using this information we can get the length of train.
So, we can eliminate options B, C, E.

2) Lb + Lt = 90*35 = 3150 & Lb = 4La => 4La + Lt = 3150
Using these details we can get the answer hence, we can eliminate option A.

Answer: D. EACH statement ALONE is sufficient to answer the question asked.

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As an initial matter, this question threw me off quite a bit at the beginning because of the difficulty I commonly associate with speed-distance questions that have tunnels/bridges in them. But once I could visualize the situation, it was no longer that hard.

Solution: It helps me to visualize this question before attempting it. Remove the bridge from the picture. The travelled distance in this question begins at the point where the head of the train enters the bridge and ends at the point where the head of the train is when end of the train leaves the bridge. Put differently, the travelled distance is the length of Bridge A and the length of the train.

Notice that the train "crosses Bridge A in 10 seconds, from the moment it enters the bridge to the moment its last carriage exits the bridge." This implies that at the speed of 90 m/s, the travelled distance is 10 * 90 = 900 m. Note that 900 m is thus the sum of the length of the train and the length of Bridge A. With that, we consider the statements.

Consider Statement (1). This information readily helps us find the length of the train, because with the ratio of the length of the train to that of the bridge be 1 to 5, and the sum of the two be 900 m, the length of the train is simply (900/6). Therefore, Statement (1) suffices to answer the question.

Consdier Statement (2). Because the train took 35 seconds to cross B, the sum of the length of the train and B is (35 * 90) m. Subtract 900 from this, we will find the difference between the length of A and B. Because we are told that B is four times longer than A, we can easily find the length of A. The substract the length of A from 900, we find the length of the train. Therefore, Statement (2) also suffices to answer the question.

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11 Jul 2024, 21:17

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From the task we understand that the distance covered by the train equals to the length of the bridge b plus the length of the train itself l, because the train starts from the first car but finishes with the last (meaning the first car is already way away from the bridge)
$S = b+l = 90*10 = 900$

Therefore, knowing b or l would help us solve the task.

Quote:

(1) The length of Bridge A is five times the length of the train.

If $b=5l,$ then $ 5l+l = 6l=900$ and we can easily find l. Sufficient by itself.

Quote:

(2) During the journey, the train crosses Bridge B, which is four times the length of Bridge A, in 35 seconds.

For bridge B we can say that: $b_1 + l = 35*90 = 3150,$ were $b_1 = 4b$ (assuming the speed always remains constant)
Therefore, $4b + l = 2250 $ and we still know that $ b + l = 900$
Subtracting the second equation from the first we get $3b = 2250 $ and $ b = 750$
As we can now easily input it into initial equation, this is sufficient by itself.

The right answer is D.

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11 Jul 2024, 21:39

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Given that the train travels at 90 meters per second and crosses Bridge A in 10 seconds, the total distance covered is:

\[
90 \text{ m/s} \times 10 \text{ s} = 900 \text{ meters}
\]

Thus, the equation is:

\[
L + B_A = 900 \text{ meters}
\]

### Statement (1):
The length of Bridge A is five times the length of the train.

\[
B_A = 5L
\]

Substituting into the equation:

\[
L + 5L = 900 \implies 6L = 900 \implies L = 150 \text{ meters}
\]

Statement (1) alone is sufficient.

### Statement (2):
Bridge B is four times the length of Bridge A, and the train crosses Bridge B in 35 seconds.

\[
B_B = 4B_A
\]

The total distance for Bridge B is:

\[
90 \text{ m/s} \times 35 \text{ s} = 3150 \text{ meters}
\]

So:

\[
L + B_B = 3150 \implies L + 4B_A = 3150
\]

Using $ L + B_A = 900 $ and $ B_A = 900 - L $:

\[
L + 4(900 - L) = 3150 \implies L + 3600 - 4L = 3150 \implies -3L = -450 \implies L = 150 \text{ meters}
\]

Statement (2) alone is sufficient.

### Conclusion:
Each statement alone is sufficient to determine the length of the train.

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11 Jul 2024, 21:52

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Bunuel

This question was provided by GMAT Club
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We have been given all the details
we have to find out the Db+ Dt=900

Db is distance of the bridge
Dt is distance of the train
both the statements can individually help us to find the distance of the bridge

Hence the answer should be D. EACH statement ALONE is sufficient to answer the question asked.

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Bunuel

This question was provided by GMAT Club
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Let the train lenght is l, bridge lenght is b.

l+b = 900m;

Statement (1) The length of Bridge A is five times the length of the train.
b =5l; So we can find l value.
Statement (2) During the journey, the train crosses Bridge B, which is four times the length of Bridge A, in 35 seconds.

l+4b = 35*90;
We can find l value by using both equations.

Hence IMO D

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11 Jul 2024, 22:42

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distance = speed * time = 90m/s *10s = 900m
Thus, bridge A length plus the train length is => B + T = 900
St. 1 B=5T
5T+T=900 => 6T=900 => T=150. So length of the train is 150. SUFFICENT.
A is sufficient, so we need to check B to know whether D is correct.
St. 2 B2=4B
distance of B2 second bridge 90m/s *35s = 3150 m
L + 4B= 3150.
and also we have L + B= 900
Thus => 3B= 2250. B= 750 =>L =150 SUFFICIENT
Correct answer is (D)

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11 Jul 2024, 22:55

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Quote:

Given Info:-

Let x be the train length, d be the bridge length:-

(x+d)/90 = 10=>. x+d = 900, Find x.

Additional Info:-

(1) d = 5x. Plugging this into given eq. will give us x. Sufficient.
(2) (x + 4d)/90 = 35. Two equations, two variables if we take given eq. into account. Sufficient.

Correct answer is (D)

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We are trying to catch the orange team.
What a crazy leading. But, I can't wait for our comeback.
it's coming.
Let's get started with our explanation for this topic on day four:

Glance - the Question:
Question: We are dealing here with kind of Rates and distance problem.

Rephrase - Reading and Understanding the question:
Given:

Train Rate: 90 meter/second (NOT - MPH)
Seconds: 10 seconds (of crossing the bridge)

[?] We need to know the length of the train.
Ok, if the train has no Length the bridge is 90*10sec = 900 meters.
if it is 90 meter length so the bridge is 810 meters.
after understanding the differences. let's move to setting our equation:
R * T = D
90[meters][/seconds] * 10 seconds = Bridge + Train Length (L)
=> We need to know one of the variables: D or L

Solve
(1) Bridge (A) = 5 Train Length (L). A = 5L
let's put it in our equation:
90*10 = 5L + L
900 = 6L
L = 150.
Here we have an answer to our problem. The train length = 150. the bridge is 750.
Sufficient

(2) Bridge (B) = 4A. also it take 35 sec to cross it
alright, you know the drill already.
90 * 35 = 4A + L
now we have the equation from the question stem: 90 * 10 = A + L
Let make subtitute them:
4*90*10 = 4A + 4L
-
90 * 35 = 4A + L
------------------------------
450 = 3L 150 = L
Here we have again a solution. and again it is 150 L but this time the Bridge length 3000 meters.
Sufficient So our Answer is D

THE END
I hope you liked the explanation, I have tried my best here.
Let me know if you have any questions about this question or my explanation.

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Bunuel

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First, let's use the given information in the problem statement:

Speed of the train = 90 meters per second
Time to cross Bridge A = 10 seconds

From this, we can derive:

Distance covered in 10 seconds at 90 meters per second = 90×10=900 meters

This 900 meters is the sum of the length of the train (L) and the length of Bridge A (B).

Statement (1):

Length of Bridge A (B) is five times the length of the train (L): B=5L

Using the equation derived:
L+B=900
Substitute B with5L:
L+5L=900
6L=900
L=150

Statement (1) alone is sufficient to determine the length of the train.

Statement (2):

Bridge B is four times the length of Bridge A: =4B
Time to cross Bridge B = 35 seconds
Distance covered in 35 seconds at 90 meters per second = 90×35=3150 meters

This 3150 meters is the sum of the length of the train (L) and the length of Bridge B L+Bb =3150

Since Bb=4B and B=5L:
L+4(5L)=3150
L+20L=3150
21L=3150
L=150

Statement (2) alone is also sufficient to determine the length of the train.

Conclusion:
Both statements alone are sufficient to answer the question.

The correct answer is:
D. EACH statement ALONE is sufficient to answer the question asked.

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11 Jul 2024, 23:42

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Bunuel

This question was provided by GMAT Club
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To determine the length of the train, let's analyze each statement separately and then together.

### Statement (1)

The length of Bridge A is five times the length of the train.

Let:
- $ L $ be the length of the train in meters.
- $ B $ be the length of Bridge A in meters.

From Statement (1), we have:
\[ B = 5L \]

The train crosses Bridge A in 10 seconds at a constant speed of 90 meters per second.

The total distance covered while crossing the bridge is the length of the train plus the length of the bridge:
\[ \text{Total distance} = L + B \]

Since $ B = 5L $, we get:
\[ \text{Total distance} = L + 5L = 6L \]

Given the speed of the train is 90 meters per second and the time taken is 10 seconds, the total distance can also be calculated as:
\[ \text{Total distance} = 90 \times 10 = 900 \text{ meters} \]

Equating the two expressions for the total distance, we get:
\[ 6L = 900 \]

Solving for $ L $:
\[ L = \frac{900}{6} = 150 \text{ meters} \]

Thus, Statement (1) alone is sufficient to determine the length of the train.

### Statement (2)

During the journey, the train crosses Bridge B, which is four times the length of Bridge A, in 35 seconds.

Let:
- $ B $ be the length of Bridge A in meters.
- $ B_2 $ be the length of Bridge B in meters.

From Statement (2), we have:
\[ B_2 = 4B \]

The train crosses Bridge B in 35 seconds at a constant speed of 90 meters per second.

The total distance covered while crossing Bridge B is the length of the train plus the length of the bridge:
\[ \text{Total distance} = L + B_2 \]

Since $ B_2 = 4B $, we get:
\[ \text{Total distance} = L + 4B \]

Given the speed of the train is 90 meters per second and the time taken is 35 seconds, the total distance can also be calculated as:
\[ \text{Total distance} = 90 \times 35 = 3150 \text{ meters} \]

Equating the two expressions for the total distance, we get:
\[ L + 4B = 3150 \]

From Statement (1), we know:
\[ B = 5L \]

Substituting $ B = 5L $ into the equation $ L + 4B = 3150 $:
\[ L + 4(5L) = 3150 \]
\[ L + 20L = 3150 \]
\[ 21L = 3150 \]

Solving for $ L $:
\[ L = \frac{3150}{21} = 150 \text{ meters} \]

Thus, Statement (2) alone is also sufficient to determine the length of the train.

### Conclusion

Since each statement alone is sufficient to determine the length of the train, the correct answer is:

D

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12 Jul 2024, 00:09

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From the ques : len of T (L) + len of bridge A( A) = 900

Statement 1:
A=5L
L+A=900
Statement 1 is suff

Statement 2 :

len of bridge (B)= 4A
4A+T=35*90
So Statement 2 is also suffi

Ans . D

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