Three men (Tom, Peter and Jack) and three women (Eliza, Anne and Karen) are spending a few months at a hillside. They are to stay in a row of nine cottages, each one living in his or her own cottage. There are no others staying in the same row of houses.
1. Anne, Tom and Jack do not want to stay in any cottage, which is at the end of the row.
2. Eliza and Anne are unwilling to stay besides any occupied cottage..
3. Karen is next to Peter and Jack.
4. Between Anne and Jack 's cottage there is just one vacant house.
5. None of the girls occupy adjacent cottages.
6. The house occupied by Tom is next to an end cottage.
questions
1. Which of the above statements can be said to have been derived from two other statements ?
(a) Statement 1
(b) Statement 2
(c) Statement 3
(d) Statement 5
(e) Statement 6
2. How many of them occupy cottages next to a vacant cottage ?
(a) 2
(b) 3
(c) 4
(d) 5
(e) 6
3. Which among these statement(s) are true ?
I. Anne is between Eliza and Jack.
II. At the most four persons can have occupied cottages on either side of them. .
III. Tom stays besides Peter
(a) I only
(b) II only
(c) I and III only
(d) II and III only
(e) I, II and III
Answers
Three men (Tom, Peter and Jack) and three women (Eliza, Anne and Karen) are spending a few months at a hillside. They are to stay in a row of nine cottages, each one living in his or her own cottage. There are no others staying in the same row of houses.
1. Anne, Tom and Jack do not want to stay in any cottage, which is at the end of the row.
2. Eliza and Anne are unwilling to stay besides any occupied cottage..
3. Karen is next to Peter and Jack.
4. Between Anne and Jack 's cottage there is just one vacant house.
5. None of the girls occupy adjacent cottages.
6. The house occupied by Tom is next to an end cottage.
questions
1. Which of the above statements can be said to have been derived from two other statements ?
(a) Statement 1
(b) Statement 2
(c) Statement 3
(d) Statement 5
(e) Statement 6
2. How many of them occupy cottages next to a vacant cottage ?
(a) 2
(b) 3
(c) 4
(d) 5
(e) 6
3. Which among these statement(s) are true ?
I. Anne is between Eliza and Jack.
II. At the most four persons can have occupied cottages on either side of them. .
III. Tom stays besides Peter
(a) I only
(b) II only
(c) I and III only
(d) II and III only
(e) I, II and III
Following are the answers of statements.
(a) Statement 1 can be said to have been derived from two other statements.
(b) 3 of them occupy cottages next to a vacant cottage.
(d) II and III are true. Statement I is not true as Anne and Eliza do not want to stay besides any occupied cottage. Statement III is not true as the statement 6 says that the house occupied by Tom is next to an end cottage.
Statement 1 is derived from statement 6 and 5: Tom's cottage is next to an end cottage according to statement 6, and none of the girls occupy adjacent cottages according to statement 5, so Anne and Eliza's cottages cannot be at the ends of the row, which means that Tom's cottage must be at one of the ends.
From the statement 3, Karen is next to Peter and Jack, so Karen, Peter and Jack all have a vacant cottage next to them. From the statement 4, Anne has a vacant cottage next to her. So, 3 of them occupy cottages next to a vacant cottage.
Statement II is true as from the above explanation we can see that at most 4 persons can have occupied cottages on either side of them. Statement III is not true as per statement 6 Tom stays besides end cottage.
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