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.

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. S=D/T 90=(a+l)/10 a+l=900 l=? (I) a=5l Using, S=D/T we can put 90 = (a+l)/10 90=6l/10 To get 'l', given information is SUFFICIENT. (II) b=4a and t=35 Using, S=D/T we can put 90 = (b+l)/35 90 = (4a+l)/35 (because b=4a) To travel a+l it takes -> 10 secs To travel 4a+l it takes -> 35 secs Then we can say D would be proportional to T because the train is travelling at a constant speed. 90 = /35 To get 'l', given information is SUFFICIENT. Therefore, correct option is D.

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

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Given:
Speed of train = 90m/s
Let length of train = T m
Let length of bridge A = A m
Time to cross A from tip to tail of train = 10 secs => Dist covered = 90*10 = 900 m
A+T = 900 ------ eq1
We need T = ?

S1: A = 5T ; substitute in eq 1 and get answer. sufficient

S2: Time to cross B is 35 secs => Dist covered = 35*90 = 3150 m
B = 4A
i.e., B+T = 3150
=> 4A +T=3150
=> 4(900-T) +T = 3150.. solve and get T
Sufficient

Hence option D

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Ans D
Speed of train: 90 mps
Time to cross Bridge A:10 sec
Length of train (L)?

(1) The length of Bridge A (A) is five times the length of the train.
A=5L
(A+L)/90=10
6L/90=10
This can be solved for L
Sufficient

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

(L+A)=900 ----(1)
(L+B)=35*90=3150 ----(2)
(L+4A)=3150

Solving the equation will give value for L

Sufficient

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Bunuel

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Given,
Speed of Train (s) = 90m/s
time taken to cover bridge A (ta) = 10s
So, Length of Bridge A (la) = s * ta = 90 * 10 = 900m

To find, Length of Train (lt) = ??

(1) la = 5*lt
So, lt = 900/5 = 180m - Length of Train
Therefore, Sufficent.

(2) Length of bridge B (lb) = 4*la
Time taken to cover Bridge B (tb) = 35s
lb = 35 * 90
la = (35*90)/4
But, no relation b/w length of bridge B and length of train.
Therefore, Not Sufficient.

Therefore, A is the correct answer.

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Length of train be L, and of bridge be B
given, L+B=900

1. B=5L
so, 6L= 900, L=150...Sufficient

2. bridge b = 4B
4B+L=35*90
and already B+L=900
solving we get L=150....Sufficient

Answer D

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Bunuel

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Let length of train be x & bridge be y
So x+y = 900, be equation 1

Statement 1: 5x + x = 900
6x = 900
X = 150 mtrs
Hence, Sufficient

Statement 2:

4y + x = 3150
Solving this with eqn 1 will give value of x

Hence, both statements alone are sufficient

So option D

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11 Jul 2024, 12:48

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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.

Solution: Let's denote
The length of the train = X meters
The length of Bridge A = Y meters

The train is traveling at a constant speed of 90 meters per second. Since the train crosses Bridge A in 10 seconds, the distance covered by the train during this time includes both the length of the train and the bridge.
Thus, X + Y = 90 meters/second * 10 seconds
X + Y = 900 --------------(1)

We need to find the value X.

Statement 1: The length of Bridge A is five times the length of the train.
This means, Y = 5X
From (1)
X + Y = 900
X + 5X = 900
X = 150
SUFFICIENT

Statement 2: During the journey, the train crosses Bridge B, which is four times the length of Bridge A, in 35 seconds.
Let the length of Bridge B = Z meters
So Z = 4Y
The time to cross Bridge B is 35 seconds, so the distance covered in this time
= 90 meters/second * 35 seconds
= 3150 meters

This distance includes the length of the train and Bridge B.
Hence, X + 4Y = 3150 ------------(2)
Subtract (1) from (2)
3Y = 2250
Y = 750
Hence X = 3150 - 3000
X = 150
SUFFICIENT

The correct answer is D

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According to me it should be option A 
 
As we know the speed of train 90m/s and it crosses bridge in 10 secs, hence length of bridge should be 90*10 = 900m 
 
from A we know length of bridge = 5* length of train and as we know length of bridge we can get length of train. 
 
from B there is not mention about the bridge, hence we cannot get the relation with the train A

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The train travels at a constant speed of 90 meters per second and crosses Bridge A in 10 seconds. The total distance traveled by the train in crossing the bridge is the sum of the length of the train L and the length of the bridge A

From the given information, we know:

90 m/s×10 s=L+A

So,

900=L+A

We need to find the value of L

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

A=5L

Substituting this into the equation 900=L+A

900=L+5L900 = L + 5L900=L+5L

900=6L

L=150

So, the length of the train is 150 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.

First, we need to express the length of Bridge B in terms of the length of Bridge A:

B=4

The total distance the train travels while crossing Bridge B is:

90 m/s×35 s=L+B

3150=L+4A

We already have:

900=L+A

We can use this equation to express A in terms of L:

A=900−L

Substitute A=900−L into the equation 3150=L+4A

3150=L+4(900−L)

L=150

So, the length of the train is 150 meters.

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

Since both statements independently suff

Therefore, the correct answer is:

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

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lenght of train?

90 m/s train crosses bridge a in 10 seconds

bridge a + train = 900 m

1) bridge a = 5*train
6 train = 900 m
train=150 m

2) bridge b = 4 * bridge a

bridge b + train = 90 m/s * 35s = 3150 m

4*bridge a + train = 3150 m (-)
4*bridge a + 4 train = 3600 m (+)
3 train = 450 m
train = 150m

d. each statement alone is sufficient

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11 Jul 2024, 14:34

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v=d/t
90(mts/sec)=(bridge length+ bus lenght)mts/10sec

900mts=(bridge length+ bus lenght)mts

(1) The length of Bridge A is five times the length of the train.
bridge length = BL
bus lenght= x
BL=5x
substitude in 900mts=(bridge length+ bus lenght)mts

900=(5x+x)
900=6x
x=900/6=150 mts

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

90(mts/sec)=(bridge B length+ bus lenght)mts/35sec
3150mts=(bridge B length+ bus lenght)mts

bridge B length= L2
bus lenght=x

L2=4BL
substitute
3150mts=(4BL+x)
also from the statement we have
900mts=(bridge length+ bus lenght)mts
900mts=(BL+x)mts

now we have 2 incognitos and 2 eq
3150=(BL+x)+3BL
3150=900+3BL
BL=(3150-900)/3=
BL= 2250/3=750
BL=750
so
900=750+x
x=150
SUFFICIENT

ANS Letter D

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Bunuel

This question was provided by GMAT Club
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train travelling at constant speed of 90m/s. it crosses bridge A in 10s from entry to exit .what is length of train?

Option 1:The length of Bridge A is five times the length of the train.
distance travelled in 10s= length of bridge A + length of train = 90m/s *10s = 900m
6*length of train = 900
so length of train =150

Option 2:During the journey, the train crosses Bridge B, which is four times the length of Bridge A, in 35 seconds.
Bridge A length + length of train= distance travelled in 10s= 10*90m/s= 900m
Bridge B length = 4* Bridge A length
Distance travelled in 35s = 90m/s*35= 3150s = Bridge B length + length of train
4*Bridge A length + train length = 3150
Bridge A length + train length = 900
3 bridge A length = 2250
BridgeA length = 750
so length of train = 900-750 =150m

So D is the answer

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A very straightforward way to answer this question is to try and solve the problem.

Here we have the following information.

The constant speed of the train - 90 m/s
The time it takes to travel the distance e.g. to cross Bridge A - 10 seconds

Now for the distance, when talking about a moving vehicle, we usually refer to them as a point. When measuring distance, therefore, we measure it with respect to the vehicle as a point. In this instance, the distance is not a single point on the train rather the "moment it enters the bridge" i.e. the front end and the "moment its last carriage exits the bridge" i.e. rear end. Therefore distance here refers to the distance of Bridge A + the length of the train.

Therefore we can write distance as = A (Bridge A) + T(Train)

Now to the two statements and how they impact the solution of the problem

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

Since we know the distance is the length of Bridge A + the Train and that the bridge is five time the length of the train we can write the distance as 5T (T being the length of the Train) + T

Therefore we can write the equation as follows

$6T = 90 m/s *10 s$

$6T = 900m$

$ T =\frac{900}{6} $

$ T=150m$

So we can determine the length of the train with the information provided in statement (1)

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

Once again we can use the information provided to write two equations

The first equation can be written with the information provided in the question as

Distance: A + T
Speed: 90 m/s
Time: 10 seconds

$ A+T = 90m/s*10s$
$ A+T = 900m$

The second equation can be written with the information provided in statement (2) which states that Bridge B is four times the length of Bridge A or just 4*Bridge A and that the time of the journey is now 35 seconds instead of 10 seconds

Distance: 4*A + T
Speed: 90 m/s
Time: 35 seconds

$4*A+T = 90m/s*35s$
$4*A+T = 3150m$

We can create a system for the two equations as follows

$4*A+T = 3150m$
$ A+T = 900m$

Now lets subtract the bottom equation from the top.

$3*A = 2250m$
$ A = 750m$

Now that we know $ A = 750m$ we can quickly calculate that the Train is $ 900m-750m = 150m $

Therefore we can calculate the length of the train with the information provided in Statement (2)

In conclusion, Statement (1) alone is sufficient as Statement (2) alone is sufficient.

The answer is D

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11 Jul 2024, 15:42

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Let length of train be 't' and bridge be 'a'
speed = 90 m/s
time taken = 10 secs

i) a = 5t
Therefore, 90 = (t+a)/10 i.e. 90(10) = 6t & t = 150
Sufficient

ii) b = 4a
So, we have 2 equations & 2 variables -
90 = (b+t)/35 & 90 = (a+t)/10
After solving for t, we get t=150
Sufficient

IMO D

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Bunuel

x = length of the train
a = length of bridge A
b = length of bridge B

x+a = 90 * 10 = 900
(when the last carriage of train exits the bridge - you add the length of the train to the length of the bridge)

Statement 1 : a = 5x
x + 5x = 900. x = 150.
Sufficient

Statement 2 :

x + b = 90 *35 = 3150
b = 4a

4a + x = 3150 -----1
a + x = 900 ----- 2

eq 1 - eq 2 : a = 750.
so, x = 900 - 750 = 150
Sufficient

OPTION D

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11 Jul 2024, 17:41

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We have :
The train travels at 90 meters per second and crosses Bridge A in 10 seconds.
Suppose L = length of the train, B_A = length of Bridge A.
L + B_A = Total distance covered = 900 meters

Statement 1
Bridge A is five times the length of the train:
B_A = 5L
L + 5L = 900
L = 150
Statement 1 alone is sufficient.

Statement 2
Bridge B is four times the length of Bridge A and the train crosses it in 35 seconds:
L + B_B = L + 4B_A = 90*35 = 3150
And L + B_A = 900
Solving gives B_A = 750 and L = 150
Statement 2 alone is sufficient.

Answer: D

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Lets length of Bridge is B and length of train is T.

distance covered= B+T

Find T
B+T=90*10=900, any relation of B&T will help solve this equestion.

Option-1
B=5T
Sufficient

Option-2
4B+T=90*35
Sufficient

Ans-D

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Statement 1 is sufficient. 900/5 would give X which is length of the train. Statement 2 can help us solve for the distance of the bridge but not of the train without knowing Statement 1.

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