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01 Jul 2025, 21:01
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* Let x be Anton's time.
* Let y be Beatrice's time.
* Let z be Carl's time.
Question: Did Carl win the race? (i.e., Is z the smallest time?)
Given: x + y = z + 3
Statement (1): None of the three ran faster than 6 kilometers per hour.
* This implies each person's time (x, y, z) must be >= 30/6 = 5 hours.
* So, x >= 5, y >= 5, z >= 5.
* From x + y = z + 3:
* Since x >= 5 and y >= 5, then x + y >= 5 + 5 = 10.
* Therefore, z + 3 >= 10
==> z >= 7 hours.
* Comparing: Carl's time (z >= 7) is always greater than or equal to the minimum possible times for Anton or Beatrice (x >= 5, y >= 5).
* This means Carl cannot have the smallest time.
* Statement (1) alone is SUFFICIENT.
Statement (2): Anton finished before Beatrice.
* This means x < y.
* This statement only provides a relationship between x and y; it gives no information about z or any absolute times.
* We cannot determine if z is the smallest.
* Statement (2) alone is NOT SUFFICIENT.
Conclusion:
Statement (1) alone is sufficient.
The final answer is A
* Let y be Beatrice's time.
* Let z be Carl's time.
Question: Did Carl win the race? (i.e., Is z the smallest time?)
Given: x + y = z + 3
Statement (1): None of the three ran faster than 6 kilometers per hour.
* This implies each person's time (x, y, z) must be >= 30/6 = 5 hours.
* So, x >= 5, y >= 5, z >= 5.
* From x + y = z + 3:
* Since x >= 5 and y >= 5, then x + y >= 5 + 5 = 10.
* Therefore, z + 3 >= 10
==> z >= 7 hours.
* Comparing: Carl's time (z >= 7) is always greater than or equal to the minimum possible times for Anton or Beatrice (x >= 5, y >= 5).
* This means Carl cannot have the smallest time.
* Statement (1) alone is SUFFICIENT.
Statement (2): Anton finished before Beatrice.
* This means x < y.
* This statement only provides a relationship between x and y; it gives no information about z or any absolute times.
* We cannot determine if z is the smallest.
* Statement (2) alone is NOT SUFFICIENT.
Conclusion:
Statement (1) alone is sufficient.
The final answer is A
01 Jul 2025, 21:18
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tA+tB=tC+3
(1)
Every time (tA, tB and tC) is, at least, 5 hours (30/6).
tA+tB=tC+3 -> tC can not be less than tA and tB if all the values are, at least, 5. The answer is NO.
Statement is sufficient
(2)
Examples:
tA = 1, tB = 2.5 then tC = 0.5 The answer is YES.
tA = 1, tB = 3.5 then tC = 1.5 The answer is NO.
Statement is insufficient
The right answer is A
(1)
Every time (tA, tB and tC) is, at least, 5 hours (30/6).
tA+tB=tC+3 -> tC can not be less than tA and tB if all the values are, at least, 5. The answer is NO.
Statement is sufficient
(2)
Examples:
tA = 1, tB = 2.5 then tC = 0.5 The answer is YES.
tA = 1, tB = 3.5 then tC = 1.5 The answer is NO.
Statement is insufficient
The right answer is A
01 Jul 2025, 21:31
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