Question – 1

**Five different students are to be selected for performing individually in a stage show. The five students – A, B, C, D and E are selected for the same purpose. The order in which they perform has to be decided based on the following conditions.A and B cannot perform immediately one after the other.D must perform immediately before A or B.C must immediately perform before or after the E’s performance.**

1. If A performs first and E third, which of the following is an acceptable order?

- A. A, B, E, D and C
- B. A, C, E, B and D
- C. A, D, E, B and C
- D. A, C, E, D and B
- E. A, B, E, C and D
- Answer:D
- Answer Explanation:Option A is wrong as it violates the first rule, second rule and third rule.Option B is wrong as it violates the second rule.Option C is wrong as it violates the second and third rule.Option D is correct as it satisfies all the conditions.Option E is wrong as it violates second and third rule.

Question – 2

**Five different students are to be selected for performing individually in a stage show. The five students – A, B, C, D and E are selected for the same purpose. The order in which they perform has to be decided based on the following conditions.A and B cannot perform immediately one after the other.D must perform immediately before A or B.C must immediately perform before or after the E’s performance.**

2. If A and B are first and third respectively, determine the position of D?

- A. Second or Fourth
- B. Exactly second
- C. Exactly fourth
- D. Fifth
- E. Second or fifth
- Answer:B
- Answer Explanation:Here, A and B are at the first and third place, so to satisfy the second condition D must be at second place.Option A is wrong as it violates the second rule.Option B is correct as it satisfies the given condition.Option C is wrong as it violates the second rule.Option D is wrong as it violates the second rule.Option E is wrong as it violates the second rule.

Question – 3

**Five different students are to be selected for performing individually in a stage show. The five students – A, B, C, D and E are selected for the same purpose. The order in which they perform has to be decided based on the following conditions.A and B cannot perform immediately one after the other.D must perform immediately before A or B.C must immediately perform before or after the E’s performance.**

3. Which of the following is possible?

- A. E performs third and C performs fifth.
- B. A performs first and B performs second.
- C. C performs in between A and B with A and B at first and third positions respectively.
- D. D performs last.
- E. D performs fourth and B performs fifth.
- Answer:E
- Answer Explanation:Option A is wrong as it violates the third rule.Option B is wrong as it violates the first rule.Option C is wrong as it violates the third rule.Option D is wrong as it violates the second rule.Option E is correct as it satisfies all the given conditions.

Question – 4

4. If E performs fifth, which of the following is necessarily true?

- A. C performs fourth.
- B. D performs fourth.
- C. A performs first.
- D. B performs third.
- E. C performs third.
- Answer:A
- Answer Explanation:Option A is correct in accordance with the third rule.Option B is wrong as it violates the third rule.Option C is wrong as it is possible but not necessarily true.Option D is wrong as it is possible but not necessary.Option E is wrong as it violates the third rule.

Question – 5

5. Which of the following is a false statement?

- A. If A and B are first and third to perform, then D must perform second.
- B. If B performs fifth, D must perform fourth.
- C. If E performs second, C can perform first or third.
- D. If A performs fifth, C must perform fourth.
- E. A and B perform fourth and fifth.
- Answer:E
- Answer Explanation:Option A is wrong as is true.Option B is wrong as it is true according to the third rule.Option C is wrong as it is true as per second rule.Option D is wrong as it is true as per third rule.Option E is correct as it is a false statement violating first rule.

Question – 6

**A person has 10 boxes of four different colours. The 10 boxes include 4 boxes of red colour, three boxes of blue colour, two boxes of green colour and one box of yellow colour. This boxes needs to be arranged in a triangular formation for easy transportation. The formation includes one box in the first row, two in the second row, three in the third and four boxes in the fourth row.The arrangement should be done in accordance with the following rules.A red box cannot be placed next to the blue box in the same row.A red box cannot be placed in the fourth row.No more than two boxes of the same colour can be put in the same row.**

6. Determine the row in which both the green boxes can be placed together.

- A. Third row
- B. Second row
- C. Fourth row
- D. Third or fourth row
- E. Second or third row
- Answer:C
- Answer Explanation:Here, suppose the green boxes are placed in the second row, then we will have to place four red boxes in the first and the third row as it cannot be placed in the fourth row. For doing it, we will need to place three red boxes in the third row which violates the third rule.So, B and E cannot be the correct answersas the third rule is violatedAlso, if two green boxes are placed in the third row, then also we will need to place three blue boxes in the fourth row, thus violating the third rule.So, A and D cannot be the answer as the third rule is violated.Option C satisfies all the given conditions and thus it is a correct answer.

Question – 7

**A person has 10 boxes of four different colours. The 10 boxes include 4 boxes of red colour, three boxes of blue colour, two boxes of green colour and one box of yellow colour. This boxes needs to be arranged in a triangular formation for easy transportation. The formation includes one box in the first row, two in the second row, three in the third and four boxes in the fourth row.The arrangement should be done in accordance with the following rules.A red box cannot be placed next to the blue box in the same row.A red box cannot be placed in the fourth row.No more than two boxes of the same colour can be put in the same row.**

7. Which of the following is a possibly true statement?

- A. Two red boxes are placed along with blue box in the third row.
- B. All blue boxes are placed together.
- C. A blue box is placed in the second row.
- D. Green boxes are placed in the second row.
- E. Only red balls are placed in the second row.
- Answer:E
- Answer Explanation:Here, red balls can be arranged in three ways. 1, 1, 2 boxes in the first three rows respectively or 1, 2, 1 and 0, 2, 2 boxes in the first three rows respectively. Of these three ways, 1, 1, 2 is not possible because doing so, we will not be able to place blue box in any of the first three rows due to violation of the first rule and all the three blue boxes can’t be placed together.Thus, option C and option D are wrong and option E is necessarily true.Option A violates the first rule and Option B violates the third rule.

Question – 8

**A person has 10 boxes of four different colours. The 10 boxes include 4 boxes of red colour, three boxes of blue colour, two boxes of green colour and one box of yellow colour. This boxes needs to be arranged in a triangular formation for easy transportation. The formation includes one box in the first row, two in the second row, three in the third and four boxes in the fourth row.The arrangement should be done in accordance with the following rules.A red box cannot be placed next to the blue box in the same row.A red box cannot be placed in the fourth row.No more than two boxes of the same colour can be put in the same row.**

8. Any arrangement of boxes must have:

- A. A blue box in the first row.
- B. A yellow box in the third row.
- C. A green box in the third row.
- D. Two green boxes in the fourth row.
- E. Two blue boxes in the fourth row.
- Answer:E
- Answer Explanation:Option A is wrong as it is not necessarily true.Option B is wrong as it can be placed in the fourth row as well.Option C is wrong as it is not necessarily true, it can be placed in the fourth row too.Option D is wrong as the green boxes can be placed in third and fourth row, each having one green box.Option E is the only correct and possible answer.

Question – 9

9. Which of the following can be a possible arrangement in the third row?

- A. Three red boxes.
- B. Two red boxes and a blue box.
- C. One red box and two blue boxes.
- D. One red box, one green box in the middle and one blue box.
- E. Two green boxes in the third row and a red box.
- Answer:D
- Answer Explanation:Option A is wrong as it violates the third rule.Option B is wrong as it violates the first rule.Option C is wrong as it violates the first rule.Option D is correct as it is possible and satisfies all conditions.Option E is wrong as it will result in placing three blue boxes in the last row, thus violating the third rule.

Question – 10

10. If yellow is placed in the third row, which of the following should be the position of blue boxes?

- A. One in each of the first three rows.
- B. One in the first row and two in the last role.
- C. One in the second row and the other two in the last row.
- D. All in the fourth row.
- E. Two in the second row, one in the fourth row.
- Answer:B
- Answer Explanation:Option A is wrong as it is not possible. We will be left with three places in the first three rows for four red boxes as red boxes can’t be placed in the fourth row..Option B is correct as it satisfies all given conditions.Option C is wrong as it is necessary to place two red balls in the second row.Option D is wrong as it violates the third rule.Option E is wrong as it is necessary to place two red balls in the second row.

Question – 11

**A student needs to work on six assignments within a given period of time. The assignments – A, B, C, D, E and F needs to be completed in accordance with the following rules:The third assignment he completes must be C.He must complete B before D.He must complete A before B and before E.**

11. If the student completes assignment F first, which assignment must he complete second?

- A. A
- B. B
- C. C
- D. D
- E. E
- Answer:A
- Answer Explanation:Here, F is completed first according to the question. Also, C must be completed third according to the first rule. A must be completed before B and E according to the third rule. Also since B is completed before D, A must be completed before D. Thus, A should be completed second.Option A is correct as per the explanation.Option B is wrong as it is not possible according to the given explanation.Option C is wrong as it is not possible.Option D is wrong as it is not possible.Option E is wrong as it is not possible.

Question – 12

**A student needs to work on six assignments within a given period of time. The assignments – A, B, C, D, E and F needs to be completed in accordance with the following rules:The third assignment he completes must be C.He must complete B before D.He must complete A before B and before E.**

12. Which of the following could be the order in which the student completes his assignments?

- A. A, D, C, B, E and F
- B. A, B, D, C, E and F
- C. F, C, D, A, B and E
- D. A, B, C, D, E and F
- E. A, C, B, D, E and F
- Answer:D
- Answer Explanation:Option A is wrong as it violates the second rule.Option B is wrong as it violates the first rule.Option C is wrong as it violates the first rule.Option D is correct as it satisfies all the given conditions.Option E is wrong as it is violates the first rule.

Question – 13

**A student needs to work on six assignments within a given period of time. The assignments – A, B, C, D, E and F needs to be completed in accordance with the following rules:The third assignment he completes must be C.He must complete B before D.He must complete A before B and before E.**

13. The student could complete any of the following assignments immediately after completing C except?

- A. A
- B. B
- C. D
- D. E
- E. F
- Answer:A
- Answer Explanation:Here, A must be completed before B, D and E according to the second and third rules. Now, C is at third which leaves only three options after it. So, A cannot be completed after C.Option A is correct as per the explanation.Option B is wrong as it is possible to complete it after C.Option C is wrong as it is possible to complete it after C.Option D is wrong as it is possible to complete it after C.Option E is wrong as it is possible to complete it after C.

Question – 14

14. If the student completes D immediately before E and immediately after F, he must complete D

- A. first
- B. second
- C. fourth
- D. fifth
- E. sixth
- Answer:D
- Answer Explanation:Here, C must be completed third. So, according to the condition in question it must be completed after C. Now, since it is completed after F and before E, the only possible position is fifth.Option A is wrong as it violates the second rule.Option B is wrong as it is not possible without violating rules.Option C is wrong as it is not possible.Option D is correct as it satisfies all the given conditionsOption E is wrong as it is not possible.

Question – 15

15. Which of the following is a true statement?

- A. A is completed third
- B. B is completed last.
- C. D is completed first.
- D. F is completed third.
- E. A must be either first or second.
- Answer:E
- Answer Explanation:Option A is wrong as it violates the first rule.Option B is wrong as it violates the second rule.Option C is wrong as it violates the second rule.Option D is wrong as it violates the first rule.Option E is correct according to all the given conditions.