Question – 1

**A person has seven different coloured balls namely A, B, C, D, E, F and G and four boxes. He has to arrange the seven balls in these four boxes. The first three boxes can hold two balls and the fourth box will have only one ball. The balls should be placed in accordance with the following rules.1). C can be placed with either B or E only.2). F cannot be placed with B.3). G cannot be placed with A as well as D.**

1. Which of the following can never be placed in the fourth box?

- A. C
- B. A
- C. B
- D. E
- E. D
- Answer:A
- Answer Explanation:According to the first rule, C can be placed with either B or E, which means it can never be placed alone and hence can never be placed in the fourth box. So, the correct answer is A.Option A is correct according to the first rule.Option B is wrong as it can be placed in the fourth box, there is no restriction on that.Option C is wrong as it can also be placed in the fourth box.Option D is wrong as it can also be placed in the fourth box.Option E is wrong as it can be placed in the fourth box.

Question – 2

**A person has seven different coloured balls namely A, B, C, D, E, F and G and four boxes. He has to arrange the seven balls in these four boxes. The first three boxes can hold two balls and the fourth box will have only one ball. The balls should be placed in accordance with the following rules.1). C can be placed with either B or E only.2). F cannot be placed with B.3). G cannot be placed with A as well as D.**

2. If F is placed along with E, which of the following is true?

- A. G is placed in a box with B
- B. A is placed in a box with B.
- C. G is placed in a box with D.
- D. A is placed in the fourth box.
- E. G is placed in the fourth box.
- Answer:E
- Answer Explanation:Here, F is placed in a box with E. C can be placed either with B or E only, since E is already placed with F, C is placed with B. So, A or G cannot be placed with B. Also, G cannot be placed with A or D according to the third rule, so G will be placed in the fourth box.Option A is wrong as it violates the first 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 because if it is correct, then G will be placed with D which violates the third rule.Option E is correct as it satisfies all conditions.

Question – 3

**A person has seven different coloured balls namely A, B, C, D, E, F and G and four boxes. He has to arrange the seven balls in these four boxes. The first three boxes can hold two balls and the fourth box will have only one ball. The balls should be placed in accordance with the following rules.1). C can be placed with either B or E only.2). F cannot be placed with B.3). G cannot be placed with A as well as D.**

3. If B is placed along with A, which of the following is a false statement?

- A. C is placed with E.
- B. F is placed with G.
- C. G is placed with D.
- D. G is placed in the fourth box.
- E. D is placed in the fourth box.
- Answer:C
- Answer Explanation:Option A is wrong as it is a true statement as it does not violate any rule.Option B is wrong as F can be placed with G.Option C is correct as it is a false statement as it violates the third rule.Option D is wrong as it can be true.Option E is wrong as it can be done.

Question – 4

4. Which of the following represents a possible pairing of balls?

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

Question – 5

5. If F is placed in the fourth box, which one of the following must be placed with A?

- A. B
- B. D
- C. G
- D. E
- E. C
- Answer:B
- Answer Explanation:Here, F is placed in the fourth box. G cannot be placed with A or D, so it should be placed with either B or E. C can be placed only with B or E. Thus, A must be placed with D only. So, the correct answer is B.Option A is wrong as it violates the first rule and third rule.Option B is correct as it satisfies all the conditions.Option C is wrong as it violates the third rule.Option D is wrong as it violates first and third rule.Option E is wrong as violates the first rule.

Question – 6

**A person is asked to select four balls out of eight balls. Four of the balls – A, B, D and E – are red balls and four – J, L, M and N – are black balls. It is also known that four of the balls -A, J, M and N are large balls whereas other four -B, D, E and L are small balls.The person should select the balls keeping in mind the following points:Exactly two red balls and two black balls are selected.Exactly two large and two small balls are selected.Either M or E, or both, are selected.**

6. If L is selected, which one of the following must also be selected?

- A. A
- B. B
- C. E
- D. J
- E. N
- Answer:A
- Answer Explanation:Here, L is a black ball and also a small ball. The other three black balls are J, M and N which all are large balls. Now, we should select a red ball which is also large. Among the options, option A satisfies our condition. So, the correct answer is A.Option A is correct as it satisfies the given conditions and is necessary.Option B is wrong as it is not necessary.Option C is wrong as it is not necessary.Option D is wrong as it is not necessary.Option E is wrong as it iis not necessary.

Question – 7

**A person is asked to select four balls out of eight balls. Four of the balls – A, B, D and E – are red balls and four – J, L, M and N – are black balls. It is also known that four of the balls -A, J, M and N are large balls whereas other four -B, D, E and L are small balls.The person should select the balls keeping in mind the following points:Exactly two red balls and two black balls are selected.Exactly two large and two small balls are selected.Either M or E, or both, are selected.**

7. If A and M are selected, the other two balls selected must be

- A. a small ball which is red and a large ball which is black.
- B. a large ball and a small ball both of which are red.
- C. a small ball which is red and a small ball which is black.
- D. two small balls both of which are red.
- E. two small balls both of which are black.
- Answer:C
- Answer Explanation:Here, A and M both are large balls. Also, A is a red ball and M is a black ball. Selection of M has satisfied the third condition. To satisfy the first two conditions we need two small balls of which one is a red ball and one is a black ball. Option C satisfies the first two conditions. So, the correct answer is C.Option A is wrong as it violates the first two conditions.Option B is wrong as it violates the first two conditions.Option C is correct as it is necessary to satisfy the given conditions.Option D is wrong as it violates the first rule.Option E is wrong as it violates the first rule.

Question – 8

**A person is asked to select four balls out of eight balls. Four of the balls – A, B, D and E – are red balls and four – J, L, M and N – are black balls. It is also known that four of the balls -A, J, M and N are large balls whereas other four -B, D, E and L are small balls.The person should select the balls keeping in mind the following points:Exactly two red balls and two black balls are selected.Exactly two large and two small balls are selected.Either M or E, or both, are selected.**

8. Which one of the following is an acceptable set of four balls?

- A. A, B, L and N
- B. A, E, J and M
- C. A, J, L and M
- D. B, E, J and N
- E. D, E, L and N
- Answer:D
- Answer Explanation:Here, we have to choose a set which satisfies all the above mentioned conditions.Now, In option A, we have two red and two black balls so the first condition is satisfied. Also, we have two large balls and two small balls which satisfies second condition. Here, the third condition is not satisfied as there is neither M nor E. So, it can’t be an acceptable set.In option B, we have three large balls which violates the second condition.In option C, we have three black balls which violates the first condition.In option D, we have two red balls and two black balls, also we have two large balls and two small balls, thus the first and the second conditions are satisfied. Here, we have both M and E in the set which satisfies the third condition. Since, we are asked only one acceptable set, this is the correct answer.Option E is wrong as it violates the second rule.

Question – 9

9. If A and B are selected, which one of the following must also be selected?

- A. D
- B. J
- C. E
- D. N
- E. L
- Answer:E
- Answer Explanation:Here, A and B are red balls. Also, A is a large ball and B is a small ball. Here, we have to notice that we have to select two black balls, one of which is a large ball and other one is a small ball. Now, L is the only small black ball, so it must be selected. So, the correct option is E.Option A is wrong as it violates the first conditions.Option B is wrong as it is not necessary.Option C is wrong as it is violates the first condition.Option D is wrong as it is not necessary.Option E is correct.

Question – 10

10. If J and N are selected, which one of the following could be, but need not be, selected?

- A. A
- B. B
- C. E
- D. L
- E. M
- Answer:B
- Answer Explanation:Here, J and N are black balls and both are large balls. So, we should select a red ball which is also a small ball.Among the given options, option A, option D and option E don’t satisfy the given condition.Among option B and option C, option B is the correct choice because we need to select a ball which could be selected but not compulsorily.Here, selection of E is needed to satisfy the third condition, so it is not the required answer.

Question – 11

**A family has total seven members and they decide to go on a picnic. They have two vehicles with each having a seating capacity for four members, two in the first row and two in the second row. The male members of the family are Joseph, Brad, Andrew and John and the female members are Samantha, Candy and Emma.They should sit according to following conditions:Brad and Andrew should not travel in the same vehicle.Samantha and John are married to each other sit in the same row of the same car.Joseph always sits in the back row of the car.Emma cannot sit with a male member.**

11. If Emma sits in the back row of one car, which member must travel in the other car?

- A. Brad
- B. Andrew
- C. Joseph
- D. Candy
- E. John
- Answer:C
- Answer Explanation:Here, Joseph always sits in the back row, since Emma cannot sit with a male member, Joseph has to sit in another car.Option A is wrong as it is not necessary.Option B is wrong as it is not necessary.Option C is correct as it is necessary to satisfy the given condition.Option D is wrong as it is not necessary.Option E is wrong as it is not necessary.

Question – 12

**A family has total seven members and they decide to go on a picnic. They have two vehicles with each having a seating capacity for four members, two in the first row and two in the second row. The male members of the family are Joseph, Brad, Andrew and John and the female members are Samantha, Candy and Emma.They should sit according to following conditions:Brad and Andrew should not travel in the same vehicle.Samantha and John are married to each other sit in the same row of the same car.Joseph always sits in the back row of the car.Emma cannot sit with a male member.**

12. If Joseph sits in a row with Brad, which of the following is a false statement?

- A. Emma must travel in the other car.
- B. John sits in the same car.
- C. Candy sits in the same car.
- D. Andrew sits in the same car.
- E. Samantha sits in the same car.
- Answer:A
- Answer Explanation:Option A is wrong as it can be true. Emma can either sit in the same car or the other car.Option B is wrong as it is possible.Option C is wrong as it is possible.Option D is correct as it is a false statement violating second rule.Option E is wrong as it can happen.

Question – 13

**A family has total seven members and they decide to go on a picnic. They have two vehicles with each having a seating capacity for four members, two in the first row and two in the second row. The male members of the family are Joseph, Brad, Andrew and John and the female members are Samantha, Candy and Emma.They should sit according to following conditions:Brad and Andrew should not travel in the same vehicle.Samantha and John are married to each other sit in the same row of the same car.Joseph always sits in the back row of the car.Emma cannot sit with a male member.**

13. Which of the following is a true statement?

- A. John and Emma can never sit in the same car.
- B. Emma and Candy must always sit together.
- C. Samantha can sit in the same car as Emma.
- D. Candy and Joseph can never sit in the same car.
- E. Emma should always sit alone.
- Answer:A
- Answer Explanation:Option A is correct as it is a true statement. Brad and Andrew should always sit in different vehicle. Emma cannot sit with a male member and John and Samantha must sit together. So, it is not possible for them to sit in the same car.Option B is wrong as it is not necessary.Option C is wrong as it is not possible.Option D is wrong as they can sit in the same car, there is no restriction.Option E is wrong as she can sit with candy.

Question – 14

14. Which of the following statements will be sufficient to determine the accurate positions of the members?

- A. Emma sits in the back row of the car along with Candy.
- B. Brad and Joseph sit in the same row of the same car with Emma alone on the back row of other car.
- C. Andrew and Joseph sit in the same row of the same car with Candy in the back row of the other car.
- D. Samantha sits in the same car as Andrew.
- E. Joseph and John sit together in a car
- Answer:B
- Answer Explanation:Option A is not sufficient as we will not be able to determine the accurate position for Brad and Andrew.Option B is sufficient as we can determine accurate positions for all members.Option C is wrong as we will not be able to determine the position of few other members such as Emma, John and Samantha.Option D is wrong as it is insufficient to determine the accurate positions.Option E is also an insufficient condition.

Question – 15

15. If Emma and Andrew sit in the same car with Emma in the back row, determine the possible position of Brad?

- A. In the front row of the other car.
- B. In the front row of the same car.
- C. With Joseph in the back row in the other car.
- D. With Candy in the back row of the other car.
- E. With Emma in the back row of the car.
- Answer:C
- Answer Explanation:If Emma and Andrew sit in the same car with Emma in the back row, then Brad will sit with Joseph in the back row of the other car. Here, Brad and Andrew have to sit in different cars. Also, to satisfy first rule, John and Samantha cannot sit in the car in which Emma is sitting. So, Brad shoud sit with Joseph in the back row.Option A is wrong as it is not possible.Option B is wrong as it violates the second rule.Option C is correct as it satisfies all the given conditions.Option D is wrong as is not possible under given circumstances.Option E is wrong as it violates the fourth rule.