Explanation

A's rate = 1/6, B's rate = 1/4; together = 5/12 of the work per hour.

In 2 hours, they complete 10/12 = 5/6 of the work, leaving 1/6.

A alone completes 1/6 of the work in 1 hour.

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Explanation

For a round table we use (n-1)! to arrange people.  

First arrange the 3 men around the table. This can be done in (3-1)! = 2! = 2 ways.  

When 3 men are seated they create 3 places between them. Since each women must sit between 2 men, the 3 women will sit in these 3 places.  

The 3 women can be arranged in these places in 3! = 6 ways.  

Therefore total number of ways = 2 × 6 = 12 ways.

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Explanation

Floor changes: 10 → 9 → 11 → 8 → 12 → 7 → 13

Net change = −1 + 2 − 3 + 4 − 5 + 6 = +3

Starting from the 10th floor, the elevator reaches the 13th floor.

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Explanation

The number of circular arrangements of n distinct people is (n − 1)!

For 5 children: (5 − 1)! = 4! = 24

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Explanation

Each office has 8 seats.

To fit 34 people:

34 ÷ 8 = 4 offices with 32 seats, and you’ll still need 2 more seats.

So you need 5 offices.

4 offices = 32 seats  

5 offices = 40 seats → enough for all 34 people

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