Multiple choice

Passage

Directions: In the following problem, you have to find out which of the given statements is/are necessary for determining the answer of the question asked.

In how many days can 20 women finish the work? I. 20 men finish the work in 8 days. II. 20 men and 20 women finish the work in 24/7 days.

  1. Either I or II

  2. Only II

  3. Only I

  4. Both I and II

  5. Neither I nor II
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let M and W be the work rates of a man and a woman. From I: 20M * 8 = 1 => M = 1/160. From II: 20M + 20W = 1 / (24/7) = 7/24. Substituting M: 20(1/160) + 20W = 7/24 => 1/8 + 20W = 7/24 => 20W = 7/24 - 3/24 = 4/24 = 1/6. So 20W = 1/6, meaning 20 women take 6 days. Both statements are required.

AI explanation

To find the time for 20 women, we need the relationship between the work rates of men and women. Statement I alone only gives the rate for 20 men as 1/8 of the work per day, which is insufficient. Statement II provides the combined rate of 20 men and 20 women as 7/24 of the work per day, but without knowing the exact rate of the 20 men from the first statement, the specific rate of the women cannot be isolated. Therefore, both statements must be used together to subtract the men's work rate from the combined rate to find the women's work rate.

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