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

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12 Jul 2024, 00:13

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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?
L of bridge A (x) + l of train (L)=90*10=900

(1) The length of Bridge A is five times the length of the train.
5L+L=900 so we can solve for L. suff

(2) During the journey, the train crosses Bridge B, which is four times the length of Bridge A, in 35 seconds.
L+4x =90*35=3150
Solving the two st together :3x=2250
x= 750
Hence L= 900-750=150
Suff

Ans D

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12 Jul 2024, 00:27

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Answer: D

Speed of train = 90m/s

Time to cross Bridge A = 10 seconds

Distance covered = (L+l), where L: Length of Bridge A, l: Length of train.

=> L+l = 90*10 = 900m.

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

L = 5l. Putting in the above equation we will get a value for l.

Therefore, statement (1) alone is sufficient.

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

=> Lb+l = 90*35 = 3150

Given Lb = 4L.

=> 4L+l = 3150

Also, L+l = 900. These two can be solved to get l.

Therefore, statement (2) alone is sufficient.

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12 Jul 2024, 00:35

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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.

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 ->
Let length of bridge = b
Let length of train= t
Length of bridge + Length of train = 90*10 = 900 meters
b+t = 900

Statement 1-
b = 5t
Value of t can be calculated.

Statement 2-
(4b+t)/90 = 35
We have 2 equations and 2 variables. Value of t can be calculated.

EACH statement ALONE is sufficient to answer the question asked.

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12 Jul 2024, 00:57

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Length of the train: t
Length of bridge A: a

a + t = 10 * 90 = 900

Statement 1: a = 5t

=> 6t = 900

=> Can find t

=> Sufficient

Statement 2:
(i) b + t = 35 * 90 = 3150
(ii) b = 4a

=> 4a + t = 3150
We also have a + t = 900

=> Can find t

=> Sufficient

==> Answer is D

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12 Jul 2024, 01:24

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We are given in this question the speed of train (90 m/s) and the time it takes to cross Bridge A (10 sec).
We need to find the length of the train and to find this we need to know the length of Bridge A.

Let's analyse each statement now:

I. Let the length of the train be T and that of Bridge A be B(a).
We're given: B(a) = 5T.

Now, using the formula Speed = Distance/ Time, we get
90 = (T + 5T)/ 10
90 = 6T/10
T = 150m.
Sufficient.

II. B(b) = 4B(a) = 4(5T) = 20T.
S = D/t
90 = 21T/35
T = 150m.
Sufficent.

Therefore, each option is equally sufficient to find the length of the train. Hence, the answer is option (D).

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A=length of bridge A
B=length of bridge B
T=length of trial
let constant speed =90m/s

time of bridge A 10sec
(1) length of bridge A is 5 times length of trail so A=5T, trial=A/5
then speed= distance/time
so, distance=speed*time
distance of bridge A=90m/s*10sec=900m
then length of trail=900m/5=180m so the statement is sufficient
(2) length of B=4A so, length of B =4*900=3600m
then from the above equation A=5T $ T=A/5
therefore B=4A ,A=B/4 so, T=B/4/5 ,
T=B/20 so, T=3600m/20
T=180m so the statement is sufficient the answer is D. EACH statement ALONE is sufficient to answer the question asked.

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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

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

Let the length of the train be t and length of bridge A be a.
Total distance travelled is t+a metres.
Statement 1: The length of Bridge A is five times the length of the train.
a= 5t. Distance = speed * time
5t + t = 90*10
t = 150 m. Hence Statement 1 is sufficient
(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 be b
b = 4a.
t + a = 900 and 4a + t = 35*90
4a + t = 3150. The equations can be solved. Hence Statement 2 is sufficient.
Thus the answer is D EACH statement ALONE is sufficient to answer the question asked.

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12 Jul 2024, 02:30

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Bridge length= A, train length =L
A+ L =900

1- A= 5L.
L=150

2- 4A+L=35*90
Two Eqn 2 variables.

IMO D.

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12 Jul 2024, 02:35

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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

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

The moment the train is about to enter the bridge, the back end of the train can be said to have to travel the length of the train (T), and the length of the bridge A (A), in order to get to the other end of the bridge. Thus if at the speed of 90 m/s, the train takes 10 seconds to cover T+A, it follows that T+A = 900 metres.

I. This gives us a relation between T and A apart from the one that we already have, I alone is sufficient to find the length of the train. 5T + T = 900 giving T = 180 meters.
II. B = 4A, thus T+4A = 35*90 = 3150, this again leave us with two equations for the given two variables, multiplying the previous relation by 4 and subtracting this one from it we get 3T = 450 or T = 150 meters.

Each statement alone is sufficient to answer the question.

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12 Jul 2024, 03:30

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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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1) t be the train len, Ba be the length of bridge a
Ba = 5t
d = s*t
Ba+ t = 90 * 10
6 t =900
t =150
suff

2)Bb be the len of Bridge B
Bb = 4* Ba
Ba+ t = 90 * 10 ----> 1
Bb+ t = 90 * 35 = 4*Ba + t = 90* 35

mult first eq by 4 4Ba +4t = 3600
sub it with sec eq 3t = 450 t=150
suff

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12 Jul 2024, 03:56

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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?
The length of train L, its speed V=90, T the time to cross the bridge A and D is the length of the bridge.
The speed can be written as follows:

$V = \frac{(D+L)}{T} => L = VT - D $

We are looking for the value of L

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

$D = 5L => L = 1/6 VT $
The statment (1) is sufficient.

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

$V = \frac{(D' +L)}{35 }= \frac{(4D+L)}{35} => 4D+L = 35V $

and $L+D = 10*V $

The statement (2) is sufficient.

The right answer is D

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12 Jul 2024, 04:18

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Each statement is sufficient to find lenght of train

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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.

Given:

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

Let length of train be L

Statements 1: The length of Bridge A is five times the length of the train

$\frac{(L + 5L) }{ 10} = 90$
$6L = 900$
$L = 150$

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

$\frac{(L + A) }{ 10} = 90$
$\frac{(L + 4A) }{ 35} = 90$
Subtracting both equations,
$3A = 90* (35-10) $
$A = 750$

Substitute in first equation,
$L + 750 = 900$
$L = 150$

Conclusion: Both statements individually are sufficient to determine the length of the train

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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

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

Given Information

The train's speed: 90 meters per second
Time to cross Bridge A: 10 seconds

Let L be the length of the train and BA be the length of Bridge A.

The total distance the train travels while crossing Bridge A (which includes the length of the train and the length of the bridge) is given by:

L+BA=90meters/second×10seconds=900meters

Statement (1)

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

BA=5L

Substitute BA in the total distance equation:
L+5L=900
L = 150 , sufficient

Statement (2)

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

BB=4BA

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

L+BB=90meters/second×35seconds=3150meters

Substitute BB=4BA in the equation:
L+4BA=3150

we know
L+BA=900
Thus, BA=900−L

Substitute BA into the equation for Bridge B:

L+4(900−L)=3150
L=150meters

Sufficient

Therefore D is right

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Distance travelled by train from the moment it enters the bridge to the last carriage crossing = length of bridge b = length of train t

As given

(b+t)/10 = 90 m /sec
b+t = 900

From statement (1), we get an additional equation b = 2t. Along with equation 1, We can solve for t using this statement alone.
From statement (2), we get additional equation (4b+t)/35 = 90. Along with equation 1, We can solve for t using this statement alone.
Hence, answer is D.

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12 Jul 2024, 05:26

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Let length of Bridge A = X, Length of train =L
$X+ L =90*10$
$X+ L= 900$

(1) The length of Bridge A is five times the length of the train.
$X= 5L$
$X+ L= 900 $
$6L=900$
L =150

(2) During the journey, the train crosses Bridge B, which is four times the length of Bridge A, in 35 seconds.
Let length of Bridge B = Y
$Y=4X$
$4X+L =35*90$
$4X+L = 3150 - (a)$
$ 4X+ 4L = 3600 - (b)$
Solving a and b,
L=150

IMO 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?

From the question itself, we can figure out that within these 10 seconds the train traveled the length of bridge A and the length of the train itself at 90 meter per second. So, the entire length of the bridge A and the train would be 10x90= 900 meter.

(1) The length of Bridge A is five times the length of the train.
Consider (1), Let's assume the length of train is x. So, the length of bridge A would be 5x. So, certainly, 5x+x=900. And, x would be 150.
So, A is sufficient to answer the question.

(2) During the journey, the train crosses Bridge B, which is four times the length of Bridge A, in 35 seconds.
Since, the length of bridge A is unknown, we are unable to reach a conclusion based on the information.

Answer A.

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12 Jul 2024, 05:45

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Question stem gives us that,
There is a train.
Speed of train = 90 m/s
Crosses bridge A in 10 s

So, we know that when train will cross bridge, it will cover total distance of train length and bridge length.

If train length = $L$ and bridge length = $A$ then,
$A + L = 90 * 10$
$A + L = 900$

We need to find L.

Statement-1
The length of Bridge A is five times the length of the train.
So,
$A = 5L$

We know A + L = 900,
5L + L = 900
L = 150 meters.

Length of train is 150 meters.

Statement-1 is sufficient.

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

We are given that,
$B = 4A$
$B + L = 90 * 35 = 3150$

One can argue that we are not provided speed for traveling bridge B.
But I am assuming based on two things - During the journey, the train crosses Bridge B and train traveling at a constant speed.

Now,
$4A + L = 3150$
$A + L = 900$

From these 2 equations, we can find that
L = 150 meters.

Statement-2 is sufficient.

Final answer will be D

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12 Jul 2024, 06:32

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Train length = l
Bridge A length = a

(a + l)/90 = 10
a + l = 900 -------- equation 1

Statement 1: a = 5l
substituting the value of a in equation 1
5l + l = 900
6l = 900
l = 150 , sufficient

Statement 2: Bridge B length is 4 times the length of A
b = 4a
(b + l) /90 = 35
4a + l = 3150 ---------- equation 2

solving equation 1 & 2 simultaneously we can get the answer, sufficient

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12 Jul 2024, 06:49

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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?

We know that, Speed=Distance/time.
Distance or length (Train Length+ Bridge Length) = 90*10= 900

(1) The length of Bridge A is five times the length of the train.
With this, x+5x=900; Solving for x, we can find the lenght of train. Hence sufficient.

(2) During the journey, the train crosses Bridge B, which is four times the length of Bridge A, in 35 seconds.
Here,
Train Length + Bridge B length= 90*35
Train Length + 4(Length of Bridge A)=3150.
We also know, TL + LB=900.
Solving both we can find the length of train. Hence sufficient.
Hence D.

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