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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # A lunar mission is made up of x astronauts and is formed fro  Question banks Downloads My Bookmarks Reviews Important topics
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Senior Manager Joined: 20 May 2014
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A lunar mission is made up of x astronauts and is formed fro [#permalink] 00:00

Question Stats: 66% (00:42) correct 33% (02:16) wrong based on 3 sessions
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.
[Reveal] Spoiler: OA Intern Joined: 09 Oct 2017
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Re: A lunar mission is made up of x astronauts and is formed fro [#permalink]
1
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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 Target Test Prep Representative Joined: 12 Sep 2018
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Re: A lunar mission is made up of x astronauts and is formed fro [#permalink]
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Expert's post
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.

_________________

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500+ lessons 3000+ practice problems 800+ HD solutions Re: A lunar mission is made up of x astronauts and is formed fro   [#permalink] 02 Oct 2018, 18:58
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