A certain train traveled from Station A to Station B. Was the train's

A certain train traveled from Station A to Station B. Was the train's average speed on the trip less than 110 km per hour? (1km = 1000m)

(1) The train's average speed on the trip was greater than 25 meters per second.
(2) The train's average speed on the trip was less than 30 meters per second.

IMO B

Sol.

1.speed i kmph= (25*60*60)/1000=90. this mean that the avg speed is greater than 90 but is it less than 110? we dont know for sure.. it can be 91 or 92... or 150 kmph. so its insufficient.

2.speed in kmph=(30*60*60)/1000=108kmph, and this is certainly less than 110 kmph so this gives clear picture that the avg speed is less than 110.
sufficient.

Let the distance be 110 km = 110,000meters.

Statement 1: The train's average speed on the trip was greater than 25 meters per second.
(Let the train is taking maximum time at the minimum speed of 25m/s)
25 meters = 1 sec
110,000meters = x sec
X = 4400sec
1hour = 3600 sec
Yhour = 4400 sec
Y = 1.22 hour
So the train will take the maximum time of 1.22 hours for 110km.
Speed of train is > 90.16km/hour
It can be 100km/h , 110km/h, 150km/h (Not Sufficient)

Statement 2: The train's average speed on the trip was less than 30 meters per second.
(Let the train is taking minimum time at the maximum speed of 30m/s)
30 meters = 1 sec
110,000meters = x sec
X = 3666.666 sec
1hour = 3600 sec
Yhour = 3666.66 sec
Y = 1.01 hour
So the train will take the minimum time of 1.01 hours for 110km.
Speed of train is < 108.91km/hour
It will be always less than 110km/h (Sufficient)

IMO B

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_________________

From statement 1,

Avg. speed given is more than 25 m/s which when converting to km/hr is, 25*18/5 = 90; i.e., more than 90 km/hr.
Thus answer is yes when it is 109 km/hr as well as no when it is 111 km/hr.
Hence, insufficient.

From statement 2,

Avg. speed given is less than 30 m/s which when converting to km/hr is, 30*18/5 = 108; i.e., less than 108 km/hr.
Which is always true for less than 110 km/hr, whether it is 100 km/hr or 50 km/hr.
Hence this statement is sufficient to give the answer as yes.

IMO ans is B.

IMO B

(1) The train's average speed on the trip was greater than 25 meters per second.

1 Hr = 60 x 60 s = 3600 s
Avg Speed (greater than )= 25 m/s = 25/1000 km X 3600/hr = 2.5 x 36 = 90 Km/hr
May be or maynot be less than 110 Km/Hr

Not Sufficient....


(2) The train's average speed on the trip was less than 30 meters per second.

Avg Speed (less than )= 30 m/s = 30/1000 km X 3600/hr = 3 x 36 = 108 Km/hr
So Avg Speed less than 110 Km/Hr

Sufficient

A certain train traveled from Station A to Station B. Was the train's average speed on the trip less than 110 km per hour? (1km = 1000m)

(1) The train's average speed on the trip was greater than 25 meters per second.
(2) The train's average speed on the trip was less than 30 meters per second.

The question asks us that whether the average speed is less than 110 km per hour.

Statement 1: Average speed > 25 m/s
Converting it to km/hr

\(= 25 \times \frac{3600}{1000}\)

\(= 25 \times \frac{18}{5}\)

\(= 5 \times 18\)
\(= 90\) km/hr.

This statement says that the average speed > 90 km/hr.
Now it can be even 110.1 km/hr so we can not say with surety that the average speed is less than 110 km/hr.

INSUFFICIENT

Statement 2: Average speed < 30 m/s
Converting it to km/hr

\(= 30 \times \frac{3600}{1000}\)

\(= 30 \times \frac{18}{5}\)

\(= 6 \times 18\)
\(= 108\) km/hr.

This statement says that the average speed < 108 km/hr.

If the speed is less than 108 km/hr, then it WILL BE less than 110 km/hr.

SUFFICIENT

IMO, OA,B

IMO B.

To convert m/s to kmph, we multiply by 18/5.

(1) 25 m/ s = 90kmph. Average speed >90kmph. It could be 200kmph or 105kmph.

Not sufficient.

(2) 30m/s = 108 kmph. Average speed < 108kmph. Tehrefore, average speed will clearly be less than 110.

Sufficient.

110 km per hour =\(\frac{ 110*1000}{60*60}= \frac{11*100}{36 }= \frac{1100}{36}= 30.(5) \) meter per second

V < 30.(5) ???

(Statement1): V >25
V could be 26( Yes) or 31(No)
Insufficient

(Statement2): V< 30
Always true
Sufficient

Answer (B)

Posted from my mobile device

Solution

Step 1: Analyse Question Stem

• Train travelled from Station A to Station B.

o Let us assume that the average speed of the train on the trip is s (in meters per second).
• We need to find if the average speed on the trip is less than 110 km per hours.

o \(110\) km/hr \(= 110*\frac{5}{18} = 30.56\) m/s

Thus, we need to find out whether \(s < 30.56\) m/s or not.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

Statement 1: The train's average speed on the trip was greater than 25 meters per second.

• According to this statement, s > 25

o So, s can be 30, in that case, s > 25 and s < 30.56
o However, s can also be 31, in that case, s > 25 as well as s > 30.56
• We are getting contradictory results from the above.

Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.

Statement 2: The train's average speed on the trip was less than 30 meters per second.

• According to this statement, \(s < 30 ⟹ s < 30.56\)

Hence, statement 2 is sufficient.
Thus, the correct answer is Option B.
_________________

(1) insufic

25m*60*60/1000,
25*36/10, 5*18=50+40=90
avg speed > 90kmh (> or <) 110kmh

(2) sufic

30m*60*60/1000,
30*36/10, 3*36=108
avg speed < 108kmh < 110kmh

Ans (B)

A certain train traveled from Station A to Station B. Was the train's average speed on the trip less than 110 km per hour? (1km = 1000m)

Avg speed < 110 KM p H
= Avg speed < 110 * (5/18) m/sec [to convert KM p H to Meter p Sec we multiplied with 5/18]
= Avg speed < 25*(11/9) m/sec ?

(1) The train's average speed on the trip was greater than 25 meters per second.

Avg speed > 25 m ps .
but we dono whether it is < 25 * (11/9) mps or > 25 * (11/9) mps .. SO insufficient

(2) The train's average speed on the trip was less than 30 meters per second.

Avg speed < 30 m ps .
so we are sure that it is < 25 * (11/9) mps = 275/9 = 30.5 mps .. SO sufficient

So answer is B

A certain train traveled from Station A to Station B. Was the train's average speed on the trip less than 110 km per hour? (1km = 1000m)

(1) The train's average speed on the trip was greater than 25 meters per second.
(2) The train's average speed on the trip was less than 30 meters per second.

stem: speed <110km/hr

1) s>25m/s
s>90km/hr
may be lesser or greater
insufficient

2) s<30m/s
s<108km/hr
so, it is lesser than 110km/hr
sufficient

Ans B

A certain train traveled from Station A to Station B. Was the train's average speed on the trip less than 110 km per hour? (1km = 1000m)

(1) The train's average speed on the trip was greater than 25 meters per second.
25m/sec = 25*3600/1000 km/hour
90 kn/hour
INSUFFICIENT to decide whether the average speed is greater than 110km/hr

(2) The train's average speed on the trip was less than 30 meters per second.
30 m/sec = 30*3.6 = 108 km/hour
SUFFICIENT

IMO B

Ans - B

Converting 110km/hr = 30.5 m/s, we are asked if S<30.5

Statement A- S> 25, not sufficient as it can be higher
Statement B - S< 30 which means S< 30.5 also
Sufficient

Posted from my mobile device

110 km / 3.6 = 30.55 meters per second.

(1) Greater than 25 meters per second. Insufficient.

(2) Less than 30 meters per second. Sufficient.
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This is a helpful answer, thank you! Where did you get 5/18 from? I'm wondering if this is a ratio I can use in other conversion questions!
Also, on a side note, did you use a calculator to work out 30.56 or did you get that correct to 2 decimal places in your head?
Many thanks,
Seb

Anyone have tips for the fastest way to do these conversions?