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A lunar mission is made up of x astronauts and is formed from a total

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

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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
[Reveal] Spoiler: OA

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Kudos [?]: 124142 [0], given: 12072

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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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New post 17 Aug 2017, 20:42
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




Hi...

I take it that these p too are selected from existing 12 ..

When you make a team, you are actually dealing with COMBINATIONS..
So you can choose x out of 12 in 12Cx ways..
You can choose x+p out of 12 in 12C(x+p)..
But the # of missions are same so 12Cx=12C(x+p)..

But nCx=nC(n-x)..
So 12Cx=12C(12-x)=12C(x+p)...
So 12-x=x+p.....12=2x+p..
So p=12-2x=2(6-x)..
So our answer has to be an EVEN number..
ONLY C is odd..
Ans C..

Otherwise you can solve it ..
12=2x+P..
x=1, p=10
X=2, p=8..... Choice E
X=3, P=6..... Nothing but choice B. p=x+3....Also choice D
X=4, P=4..... Nothing but choice A. x=p
X=5, p=2

Only C that is 3 is not there

C
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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

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New post 18 Aug 2017, 01:13
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

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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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New post 18 Aug 2017, 01:19
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?

Kudos [?]: 7 [0], given: 124

Expert Post
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Kudos [?]: 5217 [0], given: 112

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

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New post 18 Aug 2017, 02:40
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)..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5217 [0], given: 112

Re: A lunar mission is made up of x astronauts and is formed from a total   [#permalink] 18 Aug 2017, 02:40
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