Multiple choice

$A$ and $B$ together can complete a task in $7$ days. $B$ alone can do it in $20$ days. What part of the work was carried out by $A$? $I$. $A$ completed the job alone after $A$ and $B$ worked together for $5$ days. $II$. Part of the work done by $A$ could have been done by $B$ and $C$ together in $6$ days.

  1. $I$ alone sufficient while $II$ alone not sufficient to answer
  2. $II$ alone sufficient while $I$ alone not sufficient to answer
  3. Either $I$ or $II$ alone sufficient to answer
  4. Both $I$ and $II$ are not sufficient to answer
  5. Both $I$ and $II$ are necessary to answer
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I: A+B take 7 days. If they work 5 days, they finish 5/7 of the work. A finishes the remaining 2/7 alone. This is sufficient. Statement II: Does not provide enough info to isolate A's work.

AI explanation

From the main question, A's work rate is 1/7 - 1/20, which equals 13/140 of the task per day. Statement I provides the time A and B worked together (5 days) and states A completed the rest alone, allowing you to calculate the exact portion of the task A carried out using the known combined rate for 5 days and A's individual rate for the remainder. Statement II introduces an unknown worker C and gives no information about the time or amount of work A actually performed, making it impossible to calculate A's specific share. Therefore, only statement I is sufficient to answer the question.

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