Nora and Felix are riding electric scooters at constant speeds along

Question

Nora and Felix are riding electric scooters at constant speeds along the same bike path from the same starting plaza to Central Station. Felix leaves first and by the time Nora leaves, Felix is already 14 kilometers ahead. If Nora rides faster than Felix, how long after Nora leaves will Nora be 1 kilometer ahead of Felix?

(1) Nora catches up to Felix 7 minutes after she leaves the plaza.

(2) Nora arrives at Central Station 12 minutes before Felix does.

Bunuel · Accepted Answer

GMAT Club Official Solution:

Nora and Felix are riding electric scooters at constant speeds along the same bike path from the same starting plaza to Central Station. Felix leaves first and by the time Nora leaves, Felix is already 14 kilometers ahead. If Nora rides faster than Felix, how long after Nora leaves will Nora be 1 kilometer ahead of Felix?

(1) Nora catches up to Felix 7 minutes after she leaves the plaza.

Felix is 14 km ahead when Nora leaves. If Nora catches him 7 minutes later, then Nora gains 14 km on Felix in 7 minutes. To gain the additional 1 km needed to be 1 kilometer ahead of Felix, she needs an additional 7/14 = 0.5 minutes. Thus, the total time after Nora leaves before she is 1 kilometer ahead of Felix is 7 + 0.5 = 7.5 minutes. Sufficient.

(2) Nora arrives at Central Station 12 minutes before Felix does.

Knowing only that Nora arrives 12 minutes before Felix does does not determine how long it takes her to become 1 km ahead, since that depends on the total trip distance and the two speeds. Not sufficient.

Answer: A.

snowinmay · Answer

Statement (1) alone is sufficient because it gives the time for Nora to close the 14 km gap, which is 7 minutes. The relative speed is then 14 km / 7 min = 2 km/min. To be 1 km ahead, she needs to gain an additional 15 km, which takes 15 km / 2 km/min = 7.5 minutes.

Statement (2) alone is insufficient because it relates the arrival times but does not provide enough information to determine the relative speed uniquely; multiple combinations of speeds and distances satisfy the condition.

A

Edskore · Answer

Key Concept: Relative Rate and Gap Problems in Data Sufficiency

This is a classic relative speed question dressed up in DS clothing — and the trap is in Statement 2, which feels sufficient but isn't.

Setting up the framework first:
When Nora leaves, Felix is already 14 km ahead. Since Nora is faster, she's gaining on Felix at a rate of (N − F) km/min, where N and F are their speeds. The question asks: how long until Nora is 1 km ahead of Felix? That means she needs to erase the 14 km gap AND gain an additional 1 km — a total relative gain of 15 km. So the answer = 15 ÷ (N − F). We just need to know the relative speed.

Step 1 — Test Statement 1 alone:
"Nora catches up to Felix 7 minutes after she leaves."
Catching up means she closes the full 14 km gap. So: (N − F) × 7 = 14 → N − F = 2 km/min.
Now we can answer the question: time to be 1 km ahead = 15 ÷ 2 = 7.5 minutes.
Statement 1 is SUFFICIENT.

Step 2 — Test Statement 2 alone:
"Nora arrives at Central Station 12 minutes before Felix does."
Let D = distance from plaza to Central Station. Nora's travel time = D/N. From when Nora leaves, Felix has (D − 14) km remaining, so his time = (D − 14)/F. The condition gives: (D − 14)/F − D/N = 12. This is one equation with three unknowns (D, N, F). You can construct multiple scenarios with different relative speeds that all satisfy this constraint — try D = 100 with one set of speeds, then D = 200 with another. The answer to "how long until Nora is 1 km ahead" changes across scenarios.
Statement 2 is INSUFFICIENT.

Answer: A — Statement 1 alone is sufficient.

Common trap: Statement 2 feels satisfying because "12 minutes earlier" sounds like concrete timing information. But it ties together the total distance, individual speeds, and the head-start — it doesn't isolate the relative speed. On DS, always ask: does this statement uniquely determine what I'm solving for? A time-difference at the destination doesn't pin down how fast Nora is closing in before that point.

Takeaway: In relative speed DS problems, you need the relative rate (speed difference) directly or a way to calculate it in isolation — arrival time differences almost never give you that cleanly.

Adit_ · Answer

Statement 1:
Distance between them is 0 in 7 minutes.
Lets consider Felix to be stationary then
Rel. speed*time = 14
or rel. speed*7=14
Rel.speed = 2 from this
Now when she gets 1 km ahead the same ratio of speed are going to be used or this this rel. speed = x-y will grow in multiple of 2 only 
Therefore we can find when she will be ahead of felix by taking rel. speed
SUFFICIENT.

Statement 2:
Nora arriving 12 minutes before a place where there is no distance mentioned of.
We dont know where exactly is central station and how far it is actually.
INSUFFICIENT

Answer: Option A

_______________________

Bunuel  are all these questions by default marked as 550 before the answer released? Becuase quite a few including this has trap answers.

Bunuel · Answer

Yes. When I post new questions, most of the time they are initially tagged as medium difficulty. After that, the difficulty is automatically recalibrated based on users’ attempts and performance statistics on the question. Over time, as more people answer it, the system adjusts the difficulty to reflect how challenging the question actually is.

Adit_ · Answer

Got it! Just checked the results so far and as expected I think this will be marked as hard in no time!
Also I think there are many me included many time who solve (not always) based on difficulty and I think when people see medium they tend to take it casually not aware of the fact that its just the default provisional rating.

Nora and Felix are riding electric scooters at constant speeds along

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