A regional express train normally travels from Northgate Station to

Question

A regional express train normally travels from Northgate Station to Lakeside Station by its regular route and has a fixed scheduled travel time for that route. On one day, because of track maintenance, the train traveled from Northgate to Lakeside by a detour route instead. Was the train’s travel time that day more than 2 hours longer than the scheduled travel time?

(1) The train’s average (arithmetic mean) speed on the detour route differed from its average (arithmetic mean) speed on the regular route by no more than 20 kilometers per hour.
(2) The distance the train traveled on the detour route differed from the distance on the regular route by no more than 40 kilometers.

ankushsambare · Answer

Let:
r = regular route distance
v = regular route speed
Scheduled time = r/v
Detour route:
distance = r + d
speed = v + s
Detour time = (r + d)/(v + s)
We need to know whether:
(detour time) − (regular time) > 2
Statement (1):
The average speed differed by no more than 20 km/h.
So:
|s| ≤ 20
No information about distances.
Example 1:
Regular: 100 km at 100 km/h → 1 hour
Detour: 500 km at 80 km/h → 6.25 hours
Difference > 2 hours
Example 2:
Regular: 100 km at 100 km/h → 1 hour
Detour: 120 km at 100 km/h → 1.2 hours
Difference < 2 hours
Not sufficient.
Statement (2):
Distance differed by no more than 40 km.
So:
|d| ≤ 40
No information about speed.
Example 1:
Regular: 100 km at 100 km/h → 1 hour
Detour: 140 km at 10 km/h → 14 hours
Difference > 2
Example 2:
Regular: 100 km at 100 km/h → 1 hour
Detour: 140 km at 140 km/h → 1 hour
Difference = 0
Not sufficient.
Together:
Distance changes by at most 40 km and speed changes by at most 20 km/h.
Still not enough.
Example 1:
Regular: 100 km at 100 km/h → 1 hour
Detour: 140 km at 80 km/h → 1.75 hours
Difference < 2
Example 2:
Regular: 100 km at 20 km/h → 5 hours
Detour: 140 km at 1 km/h → 140 hours
Speed differs by 19 km/h, distance differs by 40 km
Difference > 2
Both satisfy the statements but give different answers.
Therefore, the statements together are not sufficient.
Answer: E

SS990 · Answer

The answer is E

Given : train takes detour to reach a destination
To find: if DEtour time tn-t>2hrs

1) (S-20)<Sn<(S+20) so not sufficient to know tn-t
2) (d-40)<dn<(d+40) so not sufficient to know tn-t

Together to find the min and max, we take, (d-40)/(s+20) <tn<(d+40)/(S-20) ...We cant solve this either. So answer is E.

We can try tn-t where t=d/s...we will still end up with a unsolvable numerator and denominator

BongBideshini · Answer

Statement (1) 
The speeds differ by no more than 20 km/hr.
This gives only information about speeds, not distances.
Even with small speed differences, the travel time difference may be small or very large, depending on distances
 Not sufficient.

Statement (2) 
The distances differ by no more than 40 km.
This gives only information about distances, not speeds.
Even a small distance increase could add more than 2 hours if the speed is low.
 Not sufficient.

(1) + (2)

Regular:
 
 40 km at 40 km/hr => 1 hr  
If Detour:
 
 80 km at 20 km/hr => 4 hr  
 Difference = 3 hr (>2hr)

If Detour:
 
 60 km at 50 km/hr => 6/5 hr  
 Difference = 1/5 hr (<2hr)

Answer: E

Bunuel · Answer

GMAT Club Official Solution:

A regional express train normally travels from Northgate Station to Lakeside Station by its regular route and has a fixed scheduled travel time for that route. On one day, because of track maintenance, the train traveled from Northgate to Lakeside by a detour route instead. Was the train’s travel time that day more than 2 hours longer than the scheduled travel time?

Let R be the distance, in kilometers, on the regular route, and let S be the train’s average speed, in kilometers per hour, on the regular route. So the scheduled travel time is:

R/S

Let D be the distance, in kilometers, on the detour route, and let V be the train’s average speed, in kilometers per hour, on the detour route. So the travel time on the detour route is:

D/V

The question asks whether:

D/V > R/S + 2

(1) The train’s average (arithmetic mean) speed on the detour route differed from its average (arithmetic mean) speed on the regular route by no more than 20 kilometers per hour.

This gives only a limit on the difference between S and V. It gives no information about R or D, so we cannot determine whether the detour travel time was more than 2 hours longer than the scheduled travel time.

Not sufficient.

(2) The distance the train traveled on the detour route differed from the distance on the regular route by no more than 40 kilometers.

This gives only a limit on the difference between R and D. It gives no information about S or V, so we cannot determine whether the detour travel time was more than 2 hours longer than the scheduled travel time.

Not sufficient.

(1)+(2) Even together, the statements are not sufficient.

For example, suppose:

R = 200
S = 100
D = 240
V = 100

Then the scheduled travel time is:

200/100 = 2 hours

The detour travel time is:

240/100 = 2.4 hours

The detour distance differs from the regular distance by 40 kilometers, and the two average speeds differ by 0 kilometers per hour, so both statements are satisfied. But the detour travel time is not more than 2 hours longer than the scheduled travel time.

So the answer is NO.

Now suppose:

R = 40
S = 20
D = 80
V = 10

Then the scheduled travel time is:

40/20 = 2 hours

The detour travel time is:

80/10 = 8 hours

The detour distance differs from the regular distance by 40 kilometers, and the two average speeds differ by 10 kilometers per hour, so both statements are satisfied. But now the detour travel time is more than 2 hours longer than the scheduled travel time.

So the answer is YES.

Not sufficient.

Answer: E.

A regional express train normally travels from Northgate Station to

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