Multiple choice

Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer: There are three people A, B and C. Find the time taken by C to complete the whole work. Statement I : A and B together can complete the work in 16 days while B and C can complete the whole work in 20 days. Statement II : A and B together can complete the work in 16 days. Efficiency of A and B is same.

  1. If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question

  2. If the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question

  3. If the data either in statement I alone or in statement II alone is sufficient to answer the question

  4. If the data in both statements I and II together are necessary to answer the question

  5. If the data given in both statements I and II together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I: 1/(A+B) = 1/16, 1/(B+C) = 1/20. We have two equations with three variables (A, B, C), so we cannot find C alone. Statement II: A=B, 1/(A+B) = 1/16. This gives A and B, but no information about C. Combining both: A=B=8 days, then 1/8 + 1/C = 1/20. This allows solving for C.

AI explanation

Statement I provides the combined rates of (A + B) as 16 days and (B + C) as 20 days, which yields one equation with two unknown individual rates, making it insufficient alone. Statement II states A and B take 16 days and have the same efficiency, giving their individual rates as 32 days each, but it provides no information about C, making it insufficient alone. Combining both statements, we know B's rate is 32 days and (B + C)'s rate is 20 days, allowing us to find C's exact time. Therefore, data in both statements I and II together are necessary to answer the question.

Keep practicing — related questions