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