A lunar misison is made up of x astronauts and is formed from a total of 12 astronauts. A day before the launch the...

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Magoosh

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

OA C

[Scott@TargetTestPrep]

Magoosh

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

OA C

The total number of possible lunar missions before p astronauts are added is 12Cx. The total number of possible lunar missions after p astronauts are added is 12C(x+p). Since total number of possible lunar missions remain unchanged, we have:

12Cx = 12C(x+p)

Recall that we have a formula: nCx = nC(n-x). Since x + (n-x) = n and apply this to our equation, we have:

x + (x+p) = 12

2x + p = 12

Now let’s check the given answer choices (notice that we are looking for a value that can’t be p):

A) p = x

2x + x = 12

3x = 12

x = 4

This is not the choice we are looking for.

B) p = x + 3

2x + x + 3 = 12

3x = 9

x = 9

This is not the choice we are looking for.

C) p = 3

2x + 3 = 12

2x = 9

x = 4.5

Since x has to be an integer, then x can’t be 4.5, which means p can’t be 3.

Answer: C