Bunuel wrote:

A lunar mission is made up of x astronauts and is formed from a total of 12 astronauts. A day before the launch the commander of the program decides to add p astronauts to the mission. If the total number of possible lunar missions remain unchanged after the commander’s decision, then which of the following cannot be the value of p?

(A) x

(B) x + 3

(C) 3

(D) 6

(E) 8

I tried to solve it but Im not sure if I am right or not

Total = 12

so teams can be made as such

2 2 2 2 2 2 here x= 2

3 3 3 3 here x= 3

4 4 4 here x= 4

6 6 here x= 6

If p members are added then what CANT BE P?

1) x , so we need to put p= x ,

if we take x = 2 then p=2

cant be distributed equally among team of 2 as we need 6 members to add one in every team to keep same number of teams

if we take x = 3 then p=3

cant be distributed equally among team of 3 as we need 4 members to add one in every team to keep same number of teams

if we take x = 4 then p=4

cant be distributed equally among team of 4 as we need 3 members to add one in every team to keep same number of teams

if we take x = 6 then p=6

CAN be distributed equally among team of 6 as we need 2 members to add one in every team to keep same number of teams and we can distribute 6 members in 2 teams

2) x + 3 , so we need to put p = x+3 ,

if we take x = 2 then p=5

cant be distributed equally among team of 2 as we need 6 members to add one in every team to keep same number of teams

if we take x = 3 then p=6

cant be distributed equally among team of 3 as we need 4 members to add one in every team to keep same number of teams

if we take x = 4 then p=7

cant be distributed equally among team of 4 as we need 3 members to add one in every team to keep same number of teams

if we take x = 6 then p=9

cant be distributed equally among team of 6 as we need 2 members to add one in every team to keep same number of teams

3) p = 3

3 members can be divided equally when x = 4

4) p = 6

6 members can be divided equally when x= 2

5) p = 8

8 members can be divided equally when x= 3

SO ONLY B don't have all possible ways in which p can be equally divided .

B answer