Directions [Set of 6 Questions]: Certain number of people were seated...
The number of people seated to the right of A was twice the number of people seated to the left of A. There were not more than 14 people. There were seven people seated between C and G where C was to the left of A.
So we have:
Case 1:
when 3 people were seated to the left of A:
Case 2:
when 4 people were seated to the left of A:
Now, we know that 7 people were seated between C and G.
Case 1a:
Case 1b:
Case 2a:
Case 2b:
Case 2c:
Case 2d:
B was seated to the immediate left of F. Three people were seated between B and E where B was to the left of E. D was seated at one of the ends.
So case 1a, 1b, 2d are invalid.
Case 2a:
Case 2b:
Case 2c:
But we are given that even number of people were seated between A and E. Hence, only case 2b is valid. Finally, we have:
13 people were seated in the row.
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Directions [Set of 6 Questions]: Certain number of people were seated...
Given information:
- D is seated at one of the ends.
- There are seven people between C and G, with C being to the left of A.
- B is seated immediately to the left of F.
- The number of people to the right of A is twice the number of people to the left of A.
- There are not more than 14 people.
- There are three people between B and E, with B being to the left of E.
- There is an even number of people between A and E.
Step-by-step solution:
1. Let's start by drawing a diagram to represent the given information:
- D _ _ _ _ _ _ _ _ _ _
- A C _ _ _ _ _ _ G
- B _ _ _ F
- _ _ _ E
2. From the given information, we know that there are seven people between C and G. Since C is to the left of A, we can place C and G accordingly:
- D _ _ _ _ _ _ _ _ _ _
- A C _ _ _ _ _ _ G
- B _ _ _ F
- _ _ _ E
3. We also know that B is seated immediately to the left of F. So, we can place B and F accordingly:
- D _ _ _ _ _ _ _ _ _ _
- A C _ _ _ _ _ _ G
- B _ _ F
- _ _ _ E
4. The number of people to the right of A is twice the number of people to the left of A. Since there are seven people between C and G, there must be twice that number, i.e., 14 people to the right of A. Therefore, there must be 7 people to the left of A:
- D _ _ _ _ _ _ _ _ _ _
- A C _ _ _ _ _ _ G
- B _ _ F
- _ _ _ E
5. There are three people between B and E, with B being to the left of E. Since there are seven people to the left of A, and seven people to the right of A, the remaining two spots must be filled by B and E:
- D _ _ _ _ _ _ _ _ _ _
- A C _ _ _ _ _ _ G
- B _ _ F
- _ _ B E
6. There is an even number of people between A and E. Since there are three people between B and E, the remaining spot must be filled by A:
- D _ _ _ _ _ _ _ _ _ _
- A C _ _ _ _ _ _ G
- B A _ F
- _ _ B E
7. Now, we can count the number of people in the row, which is 13. Therefore, the answer is option B) 13.