A bucket is filling at a uniform speed. At what time will the bucket be full?…
2024
A bucket is filling at a uniform speed. At what time will the bucket be full? Statements: 1. The bucket was put in place at 1pm. 2. The bucket was half filled at 5pm and three-quarters full at 7pm on the same day.
- A.
Each statement alone is sufficient
- B.
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question
- C.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
- D.
Statements 1 and 2 together are not sufficient, and additional data is needed to answer the question
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Concept
A data-sufficiency statement (or combination) is sufficient only if it fixes a single, unique answer to the question asked — not merely if it looks related. For a quantity that grows at a uniform (constant) rate, any two known (time, amount) readings are enough on their own to fix both the rate and, from it, the clock time at which any other amount — including "full" — is reached. A separate starting/reference time adds no further requirement once the rate has been pinned down this way.
Application
Statement 1 alone: it fixes only the clock time the bucket was placed. It carries no reading of how much of the bucket was filled at any moment, so no filling rate can be worked out from it. Statement 1 alone cannot answer when the bucket becomes full.
Statement 2 alone: two (time, fraction-filled) readings are given — half full at 5pm and three-quarters full at 7pm. The change in fraction filled between these two known times fixes the bucket's constant filling rate: (3/4 − 1/2) over 2 hours = 1/8 of the bucket per hour.
At 5pm the bucket still needs 1/2 more to be full. At a rate of 1/8 per hour, that remaining half takes (1/2) ÷ (1/8) = 4 hours, so the bucket is full at 5pm + 4 hours = 9pm — computed entirely from Statement 2, with no reference to when the bucket was first placed.
So Statement 2 alone is sufficient to answer the question, while Statement 1 alone is not.
Cross-check
Projecting Statement 2's rate backward from 5pm to 1pm (4 hours) removes 4 × 1/8 = 1/2 from the 1/2 already filled, leaving a fill level of exactly 0 at 1pm — consistent with a bucket that starts empty when it is "put in place," as Statement 1 describes. Statement 1 corroborates this timeline but supplies no information the rate calculation from Statement 2 didn't already give.
Result
The bucket's completion time (9pm) follows entirely from the two readings in Statement 2, so Statement 2 alone is sufficient, but Statement 1 alone is not sufficient to answer the question.