Q 40. Sitting Arrangement
Eight students A, B, C, D, E, F, G and H sit around a circular table, equidistant from each other, facing the centre of the table, not necessarily in the same order.
1. B and D sit neither adjacent to C nor opposite to C.
2. A sits in between E and D, and F sits in between B and H.
Which one of the following is definitely correct?
To solve this problem, we need to arrange the students around the circular table based on the given conditions.
● Condition 1: B and D sit neither adjacent to C nor opposite to C.
● Condition 2: A sits in between E and D, and F sits in between B and H.
Let's analyze these conditions step by step:
● Step 1: Place A, E, and D. Since A is between E and D, we can have the arrangement: E - A - D.
● Step 2: Place F, B, and H. F is between B and H, so we can have the arrangement: B - F - H.
● Step 3: Consider the placement of C. Since B and D cannot be adjacent or opposite to C, C cannot be placed directly next to or opposite B or D.
● Step 4: Arrange the remaining students. We have the following possible arrangement:
○ E - A - D - G - C - B - F - H
In this arrangement:
○ A is between E and D.
○ F is between B and H.
○ B and D are neither adjacent to nor opposite C.
Now, let's evaluate the options:
● Option A: B sits in between A and G.
○ In our arrangement, B is not between A and G. So, this option is incorrect.
● Option B: C sits opposite to G.
○ In our arrangement, C is not opposite G. So, this option is incorrect.
● Option C: E sits opposite to F.
○ In our arrangement, E is not opposite F. So, this option is incorrect.
Since none of the options A, B, or C are correct based on the arrangement, the correct answer is Option D: None of the above.
Q 48. Sitting Arrangement
Six persons A, B, C, D, E and F are sitting equidistant from each other around a circular table (facing the centre of the table). Consider the Question and two Statements given below:
Question: Who is sitting on the immediate left of A?
Statement-1: B is sitting opposite to C and D is sitting opposite to E.
Statement-2: F is sitting on the immediate left of B.
Which one of the following is correct in respect of the Question and the Statements?
To determine who is sitting on the immediate left of A, we need to analyze the given statements:
● Statement-1: B is sitting opposite to C and D is sitting opposite to E.
○ This statement tells us the opposite pairs: B-C and D-E. However, it does not provide any information about the position of A or F relative to these pairs. Therefore, this statement alone is not sufficient to determine who is sitting on the immediate left of A.
● Statement-2: F is sitting on the immediate left of B.
○ This statement provides the position of F relative to B, but it does not give any information about the position of A. Without knowing where A is in relation to B and F, we cannot determine who is on the immediate left of A. Therefore, this statement alone is not sufficient.
● Combining Statement-1 and Statement-2:
○ Even when combining both statements, we have the following arrangement possibilities:
1. B opposite C, D opposite E, and F on the immediate left of B. However, A's position is still undetermined.
2. The circular nature of the arrangement allows for multiple configurations where A can be placed in different positions relative to B, C, D, E, and F.
Since neither statement alone nor both statements together provide enough information to determine the exact position of A, we cannot conclusively identify who is sitting on the immediate left of A. Therefore, the correct answer is Option D.
Q 69. Sitting Arrangement
There are 6 persons arranged in a row. Another person has to shake hands with 3 of them so that he should not shake hands with two consecutive persons. In how many distinct possible combinations can the handshakes take place?
- We just need to choose 3 persons out of 6, such that no two of them are together.
- Number of ways to choose 3 out of 6 people, without any constraints = 6c3 = (6 × 5 × 4)/(3 × 2 × 1) = 20.
- Number of ways to choose 3 out of 6 people, such that all of them are together = 4.
- Number of ways to choose 3 out of 6 people, such that two of them are together = 3 + 2 + 2 + 2 + 3 = 12.
- So, required answer = 20 – (4 + 12) = 4.
Q 69. Sitting Arrangement
Consider the following:
A, B, C, D, E, F, G and H are standing in a row facing North.
B is not neighbour of G.
F is to the immediate right of G and neighbour of E.
G is not at the extreme end.
A is sixth to the left of E.
H is sixth to the right of C.
Which one of the following is correct in respect of the above?
Let's analyze the given conditions step by step:
● Condition 1: B is not a neighbor of G.
● Condition 2: F is to the immediate right of G and is a neighbor of E.
● Condition 3: G is not at the extreme end.
● Condition 4: A is sixth to the left of E.
● Condition 5: H is sixth to the right of C.
Step-by-step arrangement:
○ Since G is not at the extreme end and F is to the immediate right of G, G can be placed in the second position from the left (position 2) or the third position from the left (position 3).
● Assume G is in position 3:
○ Then F will be in position 4.
○ E must be a neighbor of F, so E can be in position 5.
● Placing A and E:
○ A is sixth to the left of E. If E is in position 5, A will be in position 5 - 6 = -1, which is not possible.
○ Therefore, E must be in position 8 (the extreme right), making A in position 2 (8 - 6 = 2).
● Placing G and F:
○ Since E is in position 8, F must be in position 7, and G must be in position 6.
● Placing H and C:
○ H is sixth to the right of C. If H is in position 8, C must be in position 2 (8 - 6 = 2).
● Final Arrangement:
○ Position 1: B
○ Position 2: C
○ Position 3: A
○ Position 4: D
○ Position 5: G
○ Position 6: F
○ Position 7: E
○ Position 8: H
● Verification:
○ B is not a neighbor of G (Condition 1 is satisfied).
○ F is to the immediate right of G and is a neighbor of E (Condition 2 is satisfied).
○ G is not at the extreme end (Condition 3 is satisfied).
○ A is sixth to the left of E (Condition 4 is satisfied).
○ H is sixth to the right of C (Condition 5 is satisfied).
Therefore, the correct answer is Option C: G is to the immediate right of D.
Q 22. Sitting Arrangement
Five people A, B, C, D and E are seated about a round table. Every chair is spaced equidistant from adjacent chairs.
(i) C is seated next to A
(ii) A is seated two seats from D
(iii) B is not seated next to A
On the basis of above information, which of the following must be true?
1. D is seated next to B
2. E is seated next to A
3. D and C are separated by two seats
Select the correct answer using the code given below:
To solve this problem, we need to arrange the five people A, B, C, D, and E around a round table based on the given conditions.
● Condition (i): C is seated next to A.
● Condition (ii): A is seated two seats from D.
● Condition (iii): B is not seated next to A.
Let's analyze these conditions step by step:
● Step 1: Place A at any position. Since it's a round table, we can start with A at any position without loss of generality.
● Step 2: According to condition (i), C must be seated next to A. So, we have two possibilities: A-C or C-A.
● Step 3: According to condition (ii), A is seated two seats from D. This means there must be one person between A and D. So, if we have A-C, then the arrangement could be A-C-X-D or D-X-C-A. Similarly, if we have C-A, then the arrangement could be C-A-X-D or D-X-A-C.
● Step 4: According to condition (iii), B is not seated next to A. This means B cannot be in the position immediately next to A.
Now, let's evaluate the options:
● Option 1: D is seated next to B.
○ In the arrangement A-C-X-D, B can be placed in the position of X, making D next to B.
○ In the arrangement D-X-C-A, B can be placed in the position of X, making D next to B.
○ Therefore, this statement can be true.
● Option 2: E is seated next to A.
○ In the arrangement A-C-X-D, if X is B, then E must be next to A.
○ In the arrangement D-X-C-A, if X is B, then E must be next to A.
○ Therefore, this statement must be true.
● Option 3: D and C are separated by two seats.
○ In the arrangement A-C-X-D, D and C are separated by one seat.
○ In the arrangement D-X-C-A, D and C are separated by one seat.
○ Therefore, this statement is not necessarily true.
Based on the analysis, statements 1 and 2 can be true, while statement 3 is not necessarily true. Therefore, the correct answer is Option B: 1 and 2 only.
Q 11. Sitting Arrangement
Four children are sitting in a row. A is occupying the seat next to B but not next to C. If C is not sitting next to D, who is/are occupying seat/seats adjacent to D?
The arrangement, as per the given information, is possible only if C is sitting next to B and D is sitting next to A,
⸪ Two possible arrangements are D A B C or C B A D
Clearly, only A is sitting adjacent to D.
Hence, option (b) is correct
Q 19. Sitting Arrangement
Five people A, B, C, D and E are seated about a round table. Every chair is spaced equidistant from adjacent chairs.
(i) C is seated next to A.
(ii) A is seated two seats from D.
(iii) B is not seated next to A.
Which of the following must be true?
(1) D is seated next to B.
(II) E is seated next to A.
Select the correct answer from the codes given below:
To solve this problem, we need to arrange the five people A, B, C, D, and E around a round table based on the given conditions.
● Condition (i): C is seated next to A.
● Condition (ii): A is seated two seats from D.
● Condition (iii): B is not seated next to A.
Let's analyze these conditions step by step:
1. Placing A and C: Since C is seated next to A, we can place A and C in adjacent seats. Let's assume A is in position 1 and C is in position 2.
2. Placing D: According to condition (ii), A is seated two seats from D. Since we are arranging them in a circle, D can be either two seats clockwise or counterclockwise from A. Therefore, D can be in position 3 or position 5.
3. Placing B: According to condition (iii), B is not seated next to A. Therefore, B cannot be in positions 2 or 5 (if D is in position 3) or positions 2 or 3 (if D is in position 5).
4. Placing E: E will take the remaining seat after placing A, C, D, and B.
Let's consider the possible arrangements:
● Arrangement 1: A is in position 1, C is in position 2, D is in position 3, B is in position 5, and E is in position 4.
○ In this arrangement, E is seated next to A, satisfying condition (II).
○ D is seated next to B, satisfying condition (I).
● Arrangement 2: A is in position 1, C is in position 2, D is in position 5, B is in position 3, and E is in position 4.
○ In this arrangement, E is seated next to A, satisfying condition (II).
○ D is seated next to B, satisfying condition (I).
In both possible arrangements, both conditions (I) and (II) are satisfied. Therefore, the correct answer is Option C: Both I and II.