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02 Jul 2025, 02:34
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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.
This is a Yes or No question.
Did Carl win the race or is the time taken by Carl in the race less than the time taken by Anton or Beatrice
Meanwhile:
The combined time Anton and Beatrice took to finish the race was exactly 3 hours longer
Let Time taken by each of the runners be denoted thus:
Ta= Time taken by Anton
Tb=Time taken by Beatrice
Tc=Time taken by Carl
Ta + Tb=Tc + 3
Statement 1
None of the three ran faster than 6 kilometers per hour
Thus the minimum time taken by Anton or Beatrice is: (30/6)=5
So Ta >= 5, Tb >= 5
Therefore: Ta + Tb >= 10
Tc >= 10 - 3
Tc >= 7
Hence carl ran slower than the other 2 runners
Statement 1 is sufficient
Statement 2
Anton finished before Beatrice.
It means that Ta > Tb
It does not any information in relation to the time Carl took to run the race. Therfore statement 2 is insufficient
(1) None of the three ran faster than 6 kilometers per hour.
(2) Anton finished before Beatrice.
This is a Yes or No question.
Did Carl win the race or is the time taken by Carl in the race less than the time taken by Anton or Beatrice
Meanwhile:
The combined time Anton and Beatrice took to finish the race was exactly 3 hours longer
Let Time taken by each of the runners be denoted thus:
Ta= Time taken by Anton
Tb=Time taken by Beatrice
Tc=Time taken by Carl
Ta + Tb=Tc + 3
Statement 1
None of the three ran faster than 6 kilometers per hour
Thus the minimum time taken by Anton or Beatrice is: (30/6)=5
So Ta >= 5, Tb >= 5
Therefore: Ta + Tb >= 10
Tc >= 10 - 3
Tc >= 7
Hence carl ran slower than the other 2 runners
Statement 1 is sufficient
Statement 2
Anton finished before Beatrice.
It means that Ta > Tb
It does not any information in relation to the time Carl took to run the race. Therfore statement 2 is insufficient
02 Jul 2025, 02:42
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My guess is D.
(1) None of the three ran faster than 6 kilometers per hour.
(2) Anton finished before Beatrice.
Carl would finish earlier than both of them in either situation.
(1) None of the three ran faster than 6 kilometers per hour.
(2) Anton finished before Beatrice.
Carl would finish earlier than both of them in either situation.
02 Jul 2025, 02:42
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Let time taken by Anton, Beatrice, & Carl to finish the race be ta, tb, & tc
Given, d = 30 km; ta + tb = tc + 3
Considering Statement 1,
The maximum speed is mentioned as 6km/hr for all 3 of the contestants.
Let their speeds be va, vb, & vc are speeds of Anton, Beatrice, & Carl respectively. Then,
ta = 30/va; tb = 30/vb; tc = 30/vc
Assuming maximum speed for all we get,
ta >= tb >= tc >= 5 hrs.
This is the lowest time possible for all three of the candidates.
But this statement alone does not provide a conclusion on whether Carl wins the race ∴ Not Sufficient.
Considering Statement 2,
This mentions that ta < tb or va > vb but this does not provide any further insights - Not sufficient
Taking Statements 1 & 2 together,
We have,
ta >= tb >= tc >= 5 hrs. & ta < tb
ta + tb = tc + 3
Substituting values for ta, tb, & tc,
tc cannot be 5 as then tb + tc should be equal to 5 + 3 = 8, which is not possible as 5 is the minimum time taken among all 3 candidates.
∴ as per the conditions, ta = 5, tb = 6 ⟹ tc = 8
ta = 5, tb = 7 ⟹ tc = 9
ta = 6, tb = 7 ⟹ tc = 10 & this pattern continues with tc always being greater than the values of ta & tb.
In none of the cases can Carl be seen to have the lowest time taken among the 3 to complete the race, which is a requirement to win the game. So the answer is no, Carl does not win the game, in any of the cases.
∴Both the statements taken together are sufficient.
Correct option is Option C
Given, d = 30 km; ta + tb = tc + 3
Considering Statement 1,
The maximum speed is mentioned as 6km/hr for all 3 of the contestants.
Let their speeds be va, vb, & vc are speeds of Anton, Beatrice, & Carl respectively. Then,
ta = 30/va; tb = 30/vb; tc = 30/vc
Assuming maximum speed for all we get,
ta >= tb >= tc >= 5 hrs.
This is the lowest time possible for all three of the candidates.
But this statement alone does not provide a conclusion on whether Carl wins the race ∴ Not Sufficient.
Considering Statement 2,
This mentions that ta < tb or va > vb but this does not provide any further insights - Not sufficient
Taking Statements 1 & 2 together,
We have,
ta >= tb >= tc >= 5 hrs. & ta < tb
ta + tb = tc + 3
Substituting values for ta, tb, & tc,
tc cannot be 5 as then tb + tc should be equal to 5 + 3 = 8, which is not possible as 5 is the minimum time taken among all 3 candidates.
∴ as per the conditions, ta = 5, tb = 6 ⟹ tc = 8
ta = 5, tb = 7 ⟹ tc = 9
ta = 6, tb = 7 ⟹ tc = 10 & this pattern continues with tc always being greater than the values of ta & tb.
In none of the cases can Carl be seen to have the lowest time taken among the 3 to complete the race, which is a requirement to win the game. So the answer is no, Carl does not win the game, in any of the cases.
∴Both the statements taken together are sufficient.
Correct option is Option C
