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

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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?
Let T the length of train, A the length of Bridge A, B the length of Bridge B
Total Distance the train move when it cross Bridge A
T + A = 10 x 90

(1) The length of Bridge A is five times the length of the train.
A = 5T. Sufficient
(2) During the journey, the train crosses Bridge B, which is four times the length of Bridge A, in 35 seconds.
T + B = 35 x 90
B = 4A. Sufficient
Answer D

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To find - What is the length of a train?

Given - 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.

Assume L = length of a train, and A = Length of Bridge A

Distance = Speed * Time
Distance that is traveled by train during this 10 seconds = L + A
L + A = 90 * 10
L + A = 900 ------- Eq1

1st - The length of Bridge A is five times the length of the train.
A = 5L
Substitute in Eq1 and get the value for L,
6L = 900
L=150 meters
Sufficient

2nd - During the journey, the train crosses Bridge B, which is four times the length of Bridge A, in 35 seconds.
Assuming B = Length of Bridge B but B = 4A,

Distance = Speed * Time
Distance that is traveled by train during this 35 seconds = L + B
L + B = 90 * 35
L + 4A = 3150 ------- Eq2
Sovling Eq 1 and 2
3A = 2250
A = 750 meters
L = 900 - 750 = 150 meters.
Sufficient

Answer D.

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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?

Ans.
let length of train=L

A+L=90x10
A+L=900 m........(i)

We need another equation apart from (i) to solve for two variables A & L.

(1) The length of Bridge A is five times the length of the train.
A=5L...........(ii)
Sufficient

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

4A+L=35x90......(iii)
Sufficient.

Ans. is D

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11 Jul 2024, 08:53

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If length of train is t, bridge length be b. Total distance covered is t+b

Speed of 90mps and time of 10 secs in the speed equation
Speed=distance/time
90=(t+b)/10
900=t+b... (A)

Need to know t exact value

With (1) alone, b=5t
We get 1 variable if used in (A) and get exact value

With (2) alone, new variable is introduced but neither t or b is resolved

So, option A

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Time to cross bridge by train = 10 sec. & speed of train = 90 MPS
Distance = speed * time = 90*10 =100 meter
Length of the train (in meters) = T
length of Bridge A (in meters) = B

(1) The length of Bridge A is five times the length of the train.
Means B=5T
Distance covered by crossing the train in bridge = length of bridge +length of train = B+T
B+T=900, 5T+T=900, T=150.
so train length is 150 meter. Sufficient.

(2) During the journey, the train crosses Bridge B, which is four times the length of Bridge A, in 35 seconds.
length of Bridge A (in meters) = L,
As per the statement, L= 4B, Distance=90×35 =3150 meters
Distance covered by crossing the train in bridge B= length of bridge B+ length of train = L+T = 4B+T
Solve 4B+T=3150 & B+T=900, we get B= 750 & T=150.
Hence, sufficient.

Answer is D.

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11 Jul 2024, 09:14

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To solve for the length of the train, let's denote the length of the train by
L meters and the length of Bridge A by B meters.

Given:
The train crosses Bridge A in 10 seconds.
The speed of the train is 90 meters per second.
From this information, we can write the equation for the total distance covered by the train in 10 seconds as the sum of the length of the train and the length of the bridge:

Distance covered in 10 seconds
Distance covered in 10 seconds=90×10=900 meters
L+B=900

Statement (1) Analysis:
Statement (1) states that the length of Bridge A is five times the length of the train:
B=5L

Substituting
B=5L into the equation
L+B=900:

L+5L=900
6L=900
L=150
So, the length of the train is 150 meters. Statement (1) alone is sufficient.

Statement (2) Analysis:
Statement (2) states that during the journey, the train crosses Bridge B, which is four times the length of Bridge A, in 35 seconds.

First, let's express the length of Bridge B in terms of Bridge A:
Length of Bridge B
Length of Bridge B=4B

The total distance covered while crossing Bridge B in 35 seconds:
Distance covered in 35 seconds
Distance covered in 35 seconds=90×35=3150 meters

L+4B=3150

We already have
L+B=900. We need to solve these two equations together.

From
L+B=900
B=900−L

Substitute B=900−L into the equation

L+4B=3150
L+4(900−L)=3150
L+3600−4L=3150

−3L+3600=3150
−3L=−450

L=150

So, the length of the train is 150 meters. Statement (2) alone is sufficient.

Conclusion
Each statement alone is sufficient to determine the length of the train.
Therefore, the correct answer is: D

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Let x be the length of the bridge and y be length of the train.

For the train to cross the bridge entirely, it has to cover the length of the bridge as well as that of the train.

Therefore, x + y = 90*10 ......(1)

We need to find y

Statement 1: x = 5y. With this we can find both x and y from (1). Statement 1 is sufficient

Statement 2: 4x +y = 35*10. With this equation and (1) we can find x and y. Statement 2 is sufficient.

Therefore, D

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11 Jul 2024, 09:18

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The length of the bridge A+the length of the train = 900 meters
(1)
x - length of the train
5x - length of the bridge A
$6x = 900,$
$x = 150;$ (meters) - the length of the train
Statement (1) alone is sufficient

(2)
The length of the bridge A + the length of the train = 900 meters
The length of the bridge B + the length of the train = 3150 meters
x - length of the train
y - length of the bridge A
4y - length of the bridge B
$y+x=900,$
$4y+x=3150;$
Solving the equation, we receive $x=150$, $y=750;$
Statement (2) is alone sufficient

Therefore, the answer is D. EACH statement ALONE is sufficient to answer the question asked.

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11 Jul 2024, 09:32

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Let L be length of the train and B be the length of the bridge.
Given
Train covers L+B in 10 seconds
So L + B = 10*90 = 900 M
-----------------------------
S-1
B=5L
Substituting this,
L+5L = 900 M
L = 150 M
Sufficient.

S-2
L+ 4 B = 35 *90 = 3150 M
Since we know L+B = 900 M
We get 3B = 2250 M
B = 750 M
Giving L = 150 M
Sufficient.

Correct answer 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.

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

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=15px =15pxDistance=15pxSpeed=15pxTime=15pxFrom Question (Equation 1)=15pxX+L=15px90=15px10=15px =15px =15px =15px =15pxFrom statement 1=15pxX = 5 L=15px =15px =15pxSubstituting =15px5 L + L=15px90=15px10=15px =15px6 L=15px90=15px10=15pxSolving for L will give L = 150 meters=15px =15px =15px =15pxThus Sufficient. =15px =15px =15px =15px =15pxFrom statement 2. (Equation 2)=15px4 X + L=15px90=15px35=15pxEquating Equation 1 and Equation 2 as they have equal speed.=15px(4 X + L) / 35 = (X + L)/10=15pxX = 5 L=15pxThis is the same information as statement 1 hence Sufficient.
Hence the answer is D.

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s= 90m/s
Total t=10s
Let the length of the train = l
Total distance covered = length of train + length of Bridge
length of train=?

Statement 1: Bridge A = 5l
d/s=t
(5l+l)/90 = 10
we can find l
I is sufficient

Statement 1: Bridge B = 4*5l = 20l
time =35s
(20l+l)/90 = 35
we can find l
II is sufficient
Ans D

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Choice D

Given:

1. Speed of the train = 90 mts/ sec constant through out the journey
2. Crossed the bridge in 10 sec (train length included in the distance)

Question: Length of train ?

Total distance travelled in 10 sec = 90*10 = 900 mts

900 mts = (length of bridge A a) + (length of the train l)
900 = l + A ----------(1)

l = ?

Statement 1:

length of bridge A = 5 times length of train
a = 5l
l + 5l = 900

6l = 900 = 150
Sufficient

Statement 1:

During the journey, a different bridge B 4 times the length of bridge A. Time taken to cross the bridge = 35 seconds
Total distance = 35 * 90 = 3150 mts

Total distance = 4a + l = 3150 ----------(2)

2 equations and 2 variables solve to get the length of train.
Sufficient

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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.

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

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The train is traveling at 90 m/s and we know that it takes 10 seconds for it to travel across the length of the bridge AND the length of itself ("from the moment it enters the bridge to the moment its last carriage exits the bridge").

Therefore, the length of the bridge (B) + the length of the train (T) is:

$90 \frac{m}{s} * 10s = 900 m$

$B+T = 900$

Statement 1

This tells us that $B = 5T$, which we can plug into our equation:

$B+T = 900$

$5T+T = 900$

$6T = 900$

$T = 150$

-> Statement 1 alone is sufficient.

Statement 2

This tells us that $T+Bridge_B = 90*35 = 3150 meters$ and that $Bridge_B=4B$

$T+4B = 3150$

and we already know that:

$T+B = 900$ -> $B = 900-T$

With these two equations, we can solve for T:

$T+4B = 3150$
$T+4(900-T) = 3150$

$T = 150$

-> Statement 2 alone is sufficient.

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

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11 Jul 2024, 10:42

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Since the train took 10 seconds to cross the bridge from the moment it enters the bridge to the moment its last carriage exits the bridge, we can say that
in 10 seconds, the train covered the length of the bridge + length of its body (since last carriage exits the bridge)

let's say length of bridge is b and length of train is t
$speed = \frac{distance }{ time }$
$90 = \frac{b+t}{10}$

From statement 1, we get b = 5t. From this we get the value of b and t. So statement 1 alone is sufficient.

From statement 2, we get the below equation
$90 = \frac{4b + t}{35}$
we get two equations,
$4b + t = 3150 $
$b + t = 900 $
We can compute the values of b and t. Therefore, statement 2 alone is sufficient.

Since each is sufficient, the right answer choice is option 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.

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

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Let Bridge A's length= A and length of train= T
A+T = 90*10= 900m
Statement 1 says A=5T T=900/6=150
Statement 2 says B=4A 4A+T=90*35 now we have two equations and two variable. we can find the value of T.
Hence
Answer is D

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In 10 s
The total length covered in the length of bridge. And the train. Now in 10s @90m/s the total distance covered = 90x10= 900 m now (1) in sufficient because reference.of length is provided along with its relation.
,
(2) is also sufficient as the length could be found with time reference. And again the relation of length of the train and bridge B is provided, hence D.

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11 Jul 2024, 11:22

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Quote:

let length be x and length of bridge be y
$10 = \frac{x + y }{ 90}$

Statement 1:
y = 5x
$10 = \frac{x + 5x }{ 90}$

we can solve for x
Sufficient.

Statement 2:
$35 = \frac{x + 4y }{ 90}$

use this equation and original equation to solve for x
Sufficient,

D

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11 Jul 2024, 11:25

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Ans : A
Train Speed: 90 m/sec ; crosses bridge A in 10 sec from the moment it enters the bridge to the moment its last carriage exits the bridge

To find : Length of Train A

Statement 1 ) length of Bridge A (X) is five times the length of the train (T) :
X=5T
Hence Dist/Speed = time
5T+T/90= 10
Sufficient

2) New Bridge B is introduced which is four times the length of Bridge A, both bridge length is unknown hence insufficient

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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.

Let length of train be x

Let length of bridge A be A

We know that

Speed = 90 m/s

Distance travelled = Length of Bridge A - length of train = A -x

Time taken = 10 seconds

(A-x)/10 = 90

A-x = 900

Statement (1) -

A = 5x

5x-x=900

4x=900

x=225 m

Statement (1) ALONE is sufficient

Statement (2)-

(B-x)/35 = 90

And B = 4A

So, 4A-x= 3150

We know that A -x = 900

A = 900 +x (substituting this in the other equation)

4(900 +x) -x = 3150

3600 +3x = 3150

3x = 3600 - 3150 = 450

x = 450/3 = 150

Statement (2) ALONE is sufficient

Therefore, the answer is - D. EACH statement ALONE is sufficient to answer the question asked.