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# If 3 members are to be selected from a team of x members then what is

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If 3 members are to be selected from a team of x members then what is  [#permalink]

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01 Apr 2018, 01:05
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73% (01:16) correct 27% (01:52) wrong based on 221 sessions

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If 3 members are to be selected from a group of x members then what is the value of x?

1) If team of 3 members is selected from the group of x members then 30 different combinations of 3 members can be formed with 2 specific members never being together on the team
2) There are a total of 35 ways to make team of 3 members out of team of x members.

Source: www.GMATinsight.com

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Re: If 3 members are to be selected from a team of x members then what is  [#permalink]

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01 Apr 2018, 02:17
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5
If 3 members are to be selected from a group of x members then what is the value of x?

1) If team of 3 members is selected from the group of x members then 30 different combinations of 3 members can be formed with 2 specific members never being together on the team
Selecting 3 members from x =xC3
Selecting 3 when the 2 specific members are together=(x-2)C1... 2 selected from x, the remaining 1 can be selected from remaining x-2.
So cases when the 2 are not together=xC3-(x-2)C1=30...
$$\frac{x(x-1)(x-2)}{6}-(x-2)=30.....(x-2)(x^2-x-6)=180.......(x-2)(x-3)(x+2)=180=4*5*9$$
So x-2=5..x=7
Sufficient

2) There are a total of 35 ways to make team of 3 members out of team of x members.
xC3=35...
$$\frac{x(x-1)(x-2)}{6}=35......x(x-2)(x-1)=5*6*7$$
x=7
Sufficient

D
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Re: If 3 members are to be selected from a team of x members then what is  [#permalink]

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01 Apr 2018, 04:51
GMATinsight wrote:
If 3 members are to be selected from a group of x members then what is the value of x?

1) If team of 3 members is selected from the group of x members then 30 different combinations of 3 members can be formed with 2 specific members never being together on the team
2) There are a total of 35 ways to make team of 3 members out of team of x members.

Source: http://www.GMATinsight.com

we have to find x.

From1 : 2 specific members never being together=Total number of combinations- 2 specific members being together.
Total number of combinations=xC3
2 specific members being together=(x-1)C3
xC3-(x-1)C3=30

Since one equation one variable . So 1 is sufficient.

From2 : xC3=35

Again one equation one variable . So 2 is also sufficient.

No need to find value it will take your time.

So D.
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Re: If 3 members are to be selected from a team of x members then what is  [#permalink]

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08 Apr 2018, 03:22
kunalcvrce wrote:
GMATinsight wrote:
If 3 members are to be selected from a group of x members then what is the value of x?

1) If team of 3 members is selected from the group of x members then 30 different combinations of 3 members can be formed with 2 specific members never being together on the team
2) There are a total of 35 ways to make team of 3 members out of team of x members.

Source: http://www.GMATinsight.com

we have to find x.

From1 : 2 specific members never being together=Total number of combinations- 2 specific members being together.
Total number of combinations=xC3
2 specific members being together=(x-1)C3
xC3-(x-1)C3=30

Since one equation one variable . So 1 is sufficient.

From2 : xC3=35

Again one equation one variable . So 2 is also sufficient.

No need to find value it will take your time.

So D.

Isnt xC3-(x-1)C3=15??

7C3= 35 and 6C3 =20, or am I wrong?
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Re: If 3 members are to be selected from a team of x members then what is  [#permalink]

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08 Apr 2018, 04:33
1
truongvu31 wrote:
kunalcvrce wrote:
GMATinsight wrote:
If 3 members are to be selected from a group of x members then what is the value of x?

1) If team of 3 members is selected from the group of x members then 30 different combinations of 3 members can be formed with 2 specific members never being together on the team
2) There are a total of 35 ways to make team of 3 members out of team of x members.

Source: http://www.GMATinsight.com

we have to find x.

From1 : 2 specific members never being together=Total number of combinations- 2 specific members being together.
Total number of combinations=xC3
2 specific members being together=(x-1)C3
xC3-(x-1)C3=30

Since one equation one variable . So 1 is sufficient.

From2 : xC3=35

Again one equation one variable . So 2 is also sufficient.

No need to find value it will take your time.

So D.

Isnt xC3-(x-1)C3=15??

7C3= 35 and 6C3 =20, or am I wrong?

Actually, it shouldnt be (x-1)C3.. The no of ways of selecting 3 out of x, so that two specific members are together on the team = (x-2)C1.. this is because if we have already fixed two members, then we have to select remaining 1 more member out of (x-2).

So it should be xC3 - (x-1)C2 = 30
And you can check: 7C3 - 5C1 = 35-5 = 30
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Re: If 3 members are to be selected from a team of x members then what is  [#permalink]

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09 Jan 2019, 13:08
Bunuel,

Is (x-2)C1 correct in chetan2u answer ?
Re: If 3 members are to be selected from a team of x members then what is   [#permalink] 09 Jan 2019, 13:08
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