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14 May 2026, 19:00
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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.
The OA will be automatically revealed on Monday 18th of May 2026 07:00:13 PM Pacific Time Zone
(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.
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The OA will be automatically revealed on Monday 18th of May 2026 07:00:13 PM Pacific Time Zone
ankushsambare
Joined: 13 Jun 2022
Last visit: 15 May 2026
Posts: 137
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Given Kudos: 107
Location: India
Schools: ISB '27 Wharton '26 INSEAD Aug '26
GPA: 2.4
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14 May 2026, 22:42
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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
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
14 May 2026, 22:48
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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
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
