Each of the six persons - P1, P2, P3, P4, P5 and P6 - is asked to choose three different fruits out of six different fruits - Orange, Apple, Banana, Peach, Litchi and Mango. Every fruit is chosen by at least one of the six persons. No person can chose more than one fruit of any type. The number of persons who chose Orange, Apple, Banana, Peach, Litchi and Mango are 3, 2, 2, 5, X and 4 respectively.
Further, it is known that:
1. P2 has chosen exactly one fruit which P5 did not.
2. There are exactly two fruits that have been chosen by P1 as well as P3 and there are exactly three fruits that have not been chosen by P3 as well as P6.
3. P6 chose Orange and Litchi and P5 did not choose Peach.
Answer the below question based on the above hints:
1. Which of the following fruits is definitely chosen by P1?
a. Only Orange
b. Only Peach
c. Both
d. None
2. For how many persons, the three fruits chosen by them can be exactly determined?
3. Which of the following person did not choose Mango?
a. Only P2
b. Only P3
c. Only P6
d. Both P3 and P6
4. Which of the statements is definitely correct?
a. P2 choose Banana
b. P4 chose Apple
c. P2 chose Apple
d. None
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Last update on October 11, 11:31 am by Rahil Choudhary.
1) option b) Only Peach
3) option d) both P3 and P6
4) option b) P4 choose apples
Last update on October 11, 12:08 pm by Parmeshwar.
3 + 2 + 2 + 5 + 4 + X = 16 + X
Since there are 6 fruits and everyone can choose 3, so 6 x 3 =18
Hence, 16 + X = 18
X = 2
1. from 3, P6 chose Orange and Litchi.
2. from 2, it is given that there are exactly two fruits that have been chosen by P1 as well as P3.
3. Peach is chosen by 5 people and there are exactly 3 fruits that have not been chosen by P3 as well as P6 (from 2), therefore P3 as well as P6 chose Peach.
4. from 2, P3 and P1 chose Orange and Litchi.
5. Mango is chosen by 4 people, therefore except for P6 and P1, every person chose Mango.
6. P5 did not choose Peach and there is one fruit that has not been chosen by P5 but is chosen by P2, so P2 choose Peach.
7. 3 fruits chosen by P5 are Apple, Banana and Mango.
8. the number of people who chose Litchi is 2, so, P1 definitely chose Orange and Peach.
P1 = Orange, Peach, Mango
P2 = Peach, Mango
P3 = Orange, Peach, Litchi
P4 = Peach, Mango
P5 = Apple, Banana, Mango
P6 = Orange, Peach, Litchi
1. c
2. 4
3. d
4. d
The no. Of persons are 6 and the fruits are 6 and to be chosen 3 each. Therefore,total fruits =18
The no. Of persons choosing the different fruits=3+2+2+5+4+x
Since one fruit can be taken once by a person
Therefore, x=2
Now,its given p5 doesnt take peach
Therefore, all the other 5 persons has taken peach
P3 and p6 doesnt take exactly 3 fruits
It means all the three fruits are same
Now,p6 is given orange and litchi and peach too
Therefore p3 has orange litchi and peach
Since litchi was 2 . It is finished
Peach is also finished
Now, it is given p1 and p3 has two fruits same.
Also mangoes are 4 and is given to all members except p3 and p6 because the have taken their 3 fruits.
So, p1 has peach,mango and orange .
P5 has mango till now
And since two apple and two bananas are left and only one fruit of one type can be given
Therefore,p5 has apple and banana and mango
And for p2 and p4 they have peach and mango but one fruit cant be determined
So, answers are as follows:
Q1. C)
Q2. 4
Q3. D)
Q4. D)
1. from 3, P6 chose Orange and Litchi.
2. from 2, it is given that there are exactly two fruits that have been chosen by P1 as well as P3.
3. Peach is chosen by 5 people and there are exactly 3 fruits that have not been chosen by P3 as well as P6 (from 2), therefore P3 as well as P6 chose Peach.
4. from 2, P3 and P1 chose Orange and Litchi.
5. Mango is chosen by 4 people, therefore except for P6 and P1, every person chose Mango.
6. P5 did not choose Peach and there is one fruit that has not been chosen by P5 but is chosen by P2, so P2 choose Peach.
7. 3 fruits chosen by P5 are Apple, Banana and Mango.
8. the number of people who chose Litchi is 2, so, P1 definitely chose Orange and Peach.
p1 = Peach, Mango, Orange
p2 = Peach, Mango
p3 = Peach, Litchi, Orange
p4 = Mango, Peach
p5 = Banana, Mango, Apple
p6 = Orange, Litchi, Peach
1. c
2. 4
3. d
4. d