Alfred and Botham are the residents of a colony. Alfred and Botham

Question

Alfred and Botham are the residents of a colony. Alfred and Botham started simultaneously on a straight road. Is the time taken by them to meet more than 12 seconds, if Alfred moves towards Botham?

(1) The distance between Alfred and Botham is 200 m and the uniform speeds of Alfred and Botham are 30 m/s and 10 m/s respectively.
(2) Both Alfred and Botham are travelling in the same direction.

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Purnank · Answer

I think its A,

Given - Alfred (A) and Botham (B) are the residents of a colony. Alfred and Botham started simultaneously on a straight road.
Given condition doesn't specify anything about the direction of both A and B. are they moving in the same direction or in opposite direction.
Lets check conditions.

1st - The distance between Alfred and Botham is 200 m and the uniform speeds of Alfred and Botham are 30 m/s and 10 m/s respectively.
So,
A(30m/s) -----------------(200m)----------------------- B(10m/s)
but we dont know the directions about their movemens,

if we assume they moving in same direction (case 1),
A(30m/s) -> ---------(200m)------------ B(10m/s) ->
the time after they meet will be = Distance between them / Relative speed = 200 / (30 - 10) = 200 / 20 = 10.sec

And, if they moving in opposite direction towards each other (case 2),
A(30m/s) -> ---------(200m)------------ <- B(10m/s)
Relative speed now will get added = 30 + 10 = 40m/s then the time required will be = 200 / 40 = 5sec.

Also, if they moving in opposite direction away from each other (case 3),
<- A(30m/s) ---------(200m)------------ B(10m/s) ->
In this case they will never meet but this case is invalid because it contradicts with the question that specifically asked for ".......if Alfred moves towards Botham"

Hence by discarding 3rd case and consider rest 2 we can safely conclude that the time taken by them to meet is less than 12 seconds as both values are less than 12. Also, in both cases Alfred moves towards Botham. Hence Sufficient.

2nd - Both Alfred and Botham are travelling in the same direction.
Ok now we know directions but we dont have speeds or distance between them hence we cant solve. Not sufficient.

Answer A.

Rucha.Shukla · Answer

Got it now, A it is

Shwarma · Answer

Option A

A and B are moving in same direction
t= 200/ 20 = 10 so <12
A and B are moving in opposite direction
t= 200/40= 5 <12

So A is enough

ananditathakar · Answer

What about the case where the slower person is behind the faster person (positioning is not clarified in the question) when they move in the same direction? then they will only meet at the endpoint right? So we may not know the time for that

egmat · Answer

The key constraint you might be overlooking is right in the question stem itself:   'Alfred moves TOWARDS Botham.'   This fixes Alfred's direction — he is always closing the gap with Botham. So Alfred can never be the faster person running away from Botham.

Now let's test  Statement 1  alone. Distance =  200  m, Alfred's speed =  30  m/s, Botham's speed =  10  m/s.

We don't know Botham's direction, but let's check every possibility:

Case 1  — Botham moves TOWARDS Alfred (they approach each other):  Relative speed  =  30  +  10  =  40  m/s. Time =  200  /  40  =  5  seconds. Is  5  >  12 ? NO.

Case 2  — Botham moves AWAY from Alfred (same direction, Alfred chasing):  Relative speed  =  30  -  10  =  20  m/s. Time =  200  /  20  =  10  seconds. Is  10  >  12 ? NO.

Case 3  — Botham stands still:  Relative speed  =  30  m/s. Time =  200  /  30  ≈  6.67  seconds. Is  6.67  >  12 ? NO.

In ALL cases, the answer is definitively NO — the time is less than  12  seconds.  The worst-case scenario (longest time to meet) is when Botham runs away, and even then it's only  10  seconds.

Now, your specific concern —  'What if the slower person (Botham) is behind the faster person (Alfred) and both go the same direction?'  That scenario would mean Alfred is moving AWAY from Botham, which directly contradicts the question stem's condition that Alfred moves towards Botham.  So that case is simply impossible here.

Since Statement  1  gives a definitive NO regardless of Botham's direction, it is  sufficient . Statement  2  alone tells us the direction but gives no distance or speed — clearly  not sufficient .

Answer: A

Advait01 · Answer

Option A
T = Total Distance/(Speed of A + Speed of B)
T = 200/(30+10) = 200/40
T = 5 sec
Sufficient
Option B Clearly Insufficient
Therefore A

Alfred and Botham are the residents of a colony. Alfred and Botham

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GMAT Data Sufficiency (DS) Questions

Alfred and Botham are the residents of a colony. Alfred and Botham

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