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A lunar mission is made up of x astronauts and is formed fro
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09 Oct 2017, 23:15
09 Oct 2017, 23:15
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47% (01:45) correct
52% (02:12) wrong based on 21 sessions
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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
Kudos for correct solution.
(A) x
(B) x + 3
(C) 3
(D) 6
(E) 8
Kudos for correct solution.
Re: A lunar mission is made up of x astronauts and is formed fro
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10 Oct 2017, 06:39
10 Oct 2017, 06:39
2
from the problem one can infer that
12 C x = 12 C (x + p)
in such a case
either x = x + p
or 12 - x = x + p
A) x = x + x ---> x = 0
12 - x = x + x ---> x = 4 p = 4
B) x = x + x + 3 ----> x = -3 not possible
12 - x = x + x + 3 ---> 3x = 9 --> x = 3 p = 9
C) x = x + 3 ---> this equation can never be true
12 - x = x + 3 ---> 2x = 9 ---> x = 4.5. funny thing astronauts cannot be cut into half. SO this equatoin is also invalid
hence the answer is C
12 C x = 12 C (x + p)
in such a case
either x = x + p
or 12 - x = x + p
A) x = x + x ---> x = 0
12 - x = x + x ---> x = 4 p = 4
B) x = x + x + 3 ----> x = -3 not possible
12 - x = x + x + 3 ---> 3x = 9 --> x = 3 p = 9
C) x = x + 3 ---> this equation can never be true
12 - x = x + 3 ---> 2x = 9 ---> x = 4.5. funny thing astronauts cannot be cut into half. SO this equatoin is also invalid
hence the answer is C
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Re: A lunar mission is made up of x astronauts and is formed fro
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02 Oct 2018, 18:58
02 Oct 2018, 18:58
2
Expert Reply
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
(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
