Two buses, R and S, each traveling at a constant speed, departed from

Question

Two buses, R and S, each traveling at a constant speed, departed from the depot at the same time and traveled along the same route toward Central Square station. Bus R traveled faster than Bus S, reached Central Square station, turned around immediately, and began traveling back toward the depot before meeting Bus S along the route. What was the distance between the depot and Central Square station?

(1) When the two buses met, Bus S was 250 kilometers from Central Square station.
(2) Bus R traveled 3 times as fast as Bus S.

Bunuel · Accepted Answer

GMAT Club Official Solution:

Two buses, R and S, each traveling at a constant speed, departed from the depot at the same time and traveled along the same route toward Central Square station. Bus R traveled faster than Bus S, reached Central Square station, turned around immediately, and began traveling back toward the depot before meeting Bus S along the route. What was the distance between the depot and Central Square station?

(1) When the two buses met, Bus S was 250 kilometers from Central Square station.

Let the distance between the depot and Central Square station be D kilometers. So, this tells us that Bus S had traveled D - 250 kilometers. We do not know anything else. Not sufficient.

(2) Bus R traveled 3 times as fast as Bus S.

This gives only the ratio of their speeds. Not sufficient.

(1)+(2) From (1), when the buses met, Bus S had traveled D - 250 kilometers. Since Bus R traveled 3 times as fast as Bus S, in the same time Bus R had traveled 3(D - 250) kilometers.

But Bus R had gone from the depot to Central Square station and then back 250 kilometers, so Bus R had traveled D + 250 kilometers. Therefore:

3(D - 250) = D + 250
D = 500

Sufficient.

Answer: C.

thisisakr · Answer

Here we are given Rs> Ss

We need to find the distance D between depot and Station

Statement 1: we are given bus S is 250 km away from station when the two buses met. However, we have no other information so we cannot tell the distance between depot and station ——  insufficient

Statement 2: we are given bus R is 3 times as fast as bus S but no other relation is given so we can’t find the distance ——  insufficient

Together ,

We know bus R is 3 times as fast as Bus S 
Let’s assume in 1 hr bus R travels with 3s speed then bus S travels s speed

As travel time t is same for both and we know t= d/s
For R the distance travelled is D+250 (using statement 1)
For S the distance travelled is D- 250

D+250/3s= D-250/s

D+250=3 * (D-250)
D+250 = 3D - 750
2D= 1000
D=500km

Answer  C

Edskore · Answer

The concept here is classic DS: one statement gives you a ratio, the other gives an absolute value. Neither alone is enough, but combined they pin down a unique answer.

Let d = distance from depot to Central Square. When the two buses meet, call the meeting point x km from the depot.

Both buses have been traveling the same time t. Bus S is 250 km from Central Square when they meet, so S traveled d - 250 km. That means x = d - 250. Bus R traveled all the way to Central Square (d km) and then turned back to the meeting point, so R traveled d + (d - x) = d + 250 km.

1. S is 250 km from Central Square. So S traveled d - 250 and R traveled d + 250. We have a relationship between the two travel distances, but d itself is free. d = 300 gives x = 50, d = 500 gives x = 250, both are consistent. Insufficient.

2. R traveled 3 times as fast as S. Since time is equal, R's distance = 3 times S's distance. So (d + 250) = 3(d - 250)... wait, that's combining with S1 already. With S2 alone, we just know the meeting point satisfies (2d - x) = 3x, giving d = 2x. Any d works here since x can be anything proportional. Insufficient.

Together: d = 2x (from S2) and x = d - 250 (from S1). Substituting: d = 2(d - 250) = 2d - 500. So d = 500 km.

The trap is S1. "250 km from the station" feels concrete enough to solve the problem, but without knowing the speed ratio, you can't anchor d. Think of it this way: if R were 4x faster instead of 3x, the meeting point would shift and d would be different even with the same 250 km gap.

Answer: C.

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Two buses, R and S, each traveling at a constant speed, departed from

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GMAT Data Sufficiency (DS) Questions

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