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Re: A lunar mission is made up of x astronauts and is formed from a total [#permalink]
chetan2u wrote:
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


can u plz look at my solution above and tell me what I have done wrong?
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Re: A lunar mission is made up of x astronauts and is formed from a total [#permalink]
Expert Reply
rocko911 wrote:
chetan2u wrote:
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


can u plz look at my solution above and tell me what I have done wrong?


Hi..
There is a problem in understanding of the problem.
Although not very clearly mentioned, the wordings do point towards..
There are 12 astronauts. A team of x will be send on a mission. If P more astronauts are added on a mission, now totalling x+p, and the number of missions possible remain the same.
It has to mean this because otherwise if 12 is added in group of x, and then in x+p, the number of group can NEVER be the same.
Example 12 divided with 4in each group makes 3group so if you add 1 more , the number of groups can never be 4.

But in the given Q, you have to find the combinations of x astronauts and x+P astronauts when TOTAL is 12...
So 12Cx=12C(x+P)..
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Re: A lunar mission is made up of x astronauts and is formed from a total [#permalink]
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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


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
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Re: A lunar mission is made up of x astronauts and is formed from a total [#permalink]
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Re: A lunar mission is made up of x astronauts and is formed from a total [#permalink]
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