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01 Jul 2025, 08:00
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Anton, Beatrice, and Carl, each running at a constant rate, competed in a 30-kilometer race. The combined time Anton and Beatrice took to finish the race was exactly 3 hours longer than the time Carl took. Did Carl win the race?
(1) None of the three ran faster than 6 kilometers per hour.
(2) Anton finished before Beatrice.
(1) None of the three ran faster than 6 kilometers per hour.
(2) Anton finished before Beatrice.
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01 Jul 2025, 08:30
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Bunuel
GMAT Club Official Explanation:
Anton, Beatrice, and Carl, each running at a constant rate, competed in a 30-kilometer race. The combined time Anton and Beatrice took to finish the race was exactly 3 hours longer than the time Carl took. Did Carl win the race?
Let A, B, and C be the times, in hours, that Anton, Beatrice, and Carl took to finish the race, respectively. So, we are given that:
A + B = C + 3
and are asked to find whether C is the least of the three.
(1) None of the three ran faster than 6 kilometers per hour.
This implies that the minimum time anyone could take to complete the race is 30/6 = 5 hours. Thus, A + B ≥ 10.
Let's see if Carl could have won running at this maximum rate. If he ran at the fastest rate, he would finish in 5 hours, making A + B equal to C + 3 = 5 + 3 = 8 hours. However, this is impossible since we know that A + B ≥ 10. So, if Carl cannot win even running at the fastest rate, he could not have won at all. Sufficient.
(2) Anton finished before Beatrice.
This implies that Beatrice did not win. However, either Anton or Carl could have won. For example, if A = 1, B = 10, and C = 8, Anton won; but if A = 1.5, B = 2.5, and C = 1, then Carl won. Not sufficient.
Answer: A.
General Discussion
MaxFabianKirchner
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01 Jul 2025, 08:13
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Let Ta, Tb, and Tc be the finishing times for Anton, Beatrice, and Carl.
The question is: Is Tc the shortest time?
The given equation is: Ta + Tb = Tc + 3.
(1) None of the three ran faster than 6 kilometers per hour.
The race is 30 km. This means the minimum time for any runner is 30 km / 6 km/h = 5 hours.
So, Ta, Tb, and Tc are all at least 5.
Let's rearrange the given equation: Ta = Tc + 3 - Tb.
Since Tb is at least 5, the term (3 - Tb) must be -2 or less.
This means Ta <= Tc - 2.
Anton's time was at least 2 hours shorter than Carl's time, so Anton beat Carl. Carl did not win.
This gives a definite "No" answer. Statement (1) is SUFFICIENT.
(2) Anton finished before Beatrice.
This means Ta < Tb.
Let's test two scenarios with the equation Ta + Tb = Tc + 3.
Scenario A (Carl wins): Let Tc=2. Then Ta+Tb=5. If Ta=2.4 and Tb=2.6, Carl's time is the shortest. The answer is "Yes".
Scenario B (Carl loses): Let Tc=4. Then Ta+Tb=7. If Ta=3 and Tb=4, Anton's time is the shortest. The answer is "No".
Since the answer could be Yes or No, statement (2) is INSUFFICIENT.
The correct answer is (A).
The question is: Is Tc the shortest time?
The given equation is: Ta + Tb = Tc + 3.
(1) None of the three ran faster than 6 kilometers per hour.
The race is 30 km. This means the minimum time for any runner is 30 km / 6 km/h = 5 hours.
So, Ta, Tb, and Tc are all at least 5.
Let's rearrange the given equation: Ta = Tc + 3 - Tb.
Since Tb is at least 5, the term (3 - Tb) must be -2 or less.
This means Ta <= Tc - 2.
Anton's time was at least 2 hours shorter than Carl's time, so Anton beat Carl. Carl did not win.
This gives a definite "No" answer. Statement (1) is SUFFICIENT.
(2) Anton finished before Beatrice.
This means Ta < Tb.
Let's test two scenarios with the equation Ta + Tb = Tc + 3.
Scenario A (Carl wins): Let Tc=2. Then Ta+Tb=5. If Ta=2.4 and Tb=2.6, Carl's time is the shortest. The answer is "Yes".
Scenario B (Carl loses): Let Tc=4. Then Ta+Tb=7. If Ta=3 and Tb=4, Anton's time is the shortest. The answer is "No".
Since the answer could be Yes or No, statement (2) is INSUFFICIENT.
The correct answer is (A).
