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# How many organizational structures can be formed that consist of Divis

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Manager
Joined: 22 Sep 2018
Posts: 249
How many organizational structures can be formed that consist of Divis  [#permalink]

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18 Nov 2018, 19:18
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Difficulty:

95% (hard)

Question Stats:

39% (02:55) correct 61% (02:17) wrong based on 59 sessions

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How many organizational structures can be formed that consist of Division A; at least one of Divisions B and C; at least two of Divisions D, E, and F; and at least two of Divisions G, H, J, and K?

a) 60
b) 90
c) 99
d) 120
e) 132
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9218
Location: Pune, India
Re: How many organizational structures can be formed that consist of Divis  [#permalink]

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26 Nov 2018, 07:21
1
kchen1994 wrote:
How many organizational structures can be formed that consist of Division A; at least one of Divisions B and C; at least two of Divisions D, E, and F; and at least two of Divisions G, H, J, and K?

a) 60
b) 90
c) 99
d) 120
e) 132

Division A can be taken in 1 way.

Ways of selecting at least one of B and C = 2^2 - 1 = 3
Explanation: B can be picked in 2 ways (pick or not pick) and C can be picked in 2 ways (pick or not pick). This gives us 2*2 = 4 total ways. Out of this, it is not acceptable to not pick either so we remove 1.

Ways of selecting at least two of D, E and F = 2^3 - 1 - 3 = 4
Explanation: D can be picked in 2 ways (pick or not pick), E can be picked in 2 ways (pick or not pick) and F can be picked in 2 ways (pick or not pick). This gives us 2*2*2 = 8 total ways. Out of this, it is not acceptable to not pick any so we remove 1. It is also not acceptable to pick only 1 (since at least 2 have to picked) so remove 3 ways in which you can pick any one.

Ways of selecting at least 2 of G, H, J, K = 2^4 - 1 - 4 = 11
Same explanation as above.

Total = 1*3*4*11 = 132
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Karishma
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Joined: 02 Oct 2018
Posts: 57
Re: How many organizational structures can be formed that consist of Divis  [#permalink]

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26 Nov 2018, 07:26
kchen1994 wrote:
How many organizational structures can be formed that consist of Division A; at least one of Divisions B and C; at least two of Divisions D, E, and F; and at least two of Divisions G, H, J, and K?

a) 60
b) 90
c) 99
d) 120
e) 132

Division A can be taken in 1 way.

Ways of selecting at least one of B and C = 2^2 - 1 = 3
Explanation: B can be picked in 2 ways (pick or not pick) and C can be picked in 2 ways (pick or not pick). This gives us 2*2 = 4 total ways. Out of this, it is not acceptable to not pick either so we remove 1.

Ways of selecting at least two of D, E and F = 2^3 - 1 - 3 = 4
Explanation: D can be picked in 2 ways (pick or not pick), E can be picked in 2 ways (pick or not pick) and F can be picked in 2 ways (pick or not pick). This gives us 2*2*2 = 8 total ways. Out of this, it is not acceptable to not pick any so we remove 1. It is also not acceptable to pick only 1 (since at least 2 have to picked) so remove 3 ways in which you can pick any one.

Ways of selecting at least 2 of G, H, J, K = 2^4 - 1 - 4 = 11
Same explanation as above.

Total = 1*3*4*11 = 132

Understood. Thanks for a quick response VeritasKarishma
Math Expert
Joined: 02 Aug 2009
Posts: 7671
Re: How many organizational structures can be formed that consist of Divis  [#permalink]

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26 Nov 2018, 07:32
1
1
kchen1994 wrote:
How many organizational structures can be formed that consist of Division A; at least one of Divisions B and C; at least two of Divisions D, E, and F; and at least two of Divisions G, H, J, and K?

a) 60
b) 90
c) 99
d) 120
e) 132

Hi ParthSanghavi,

The way would be to see how each set will turn out to be..
consist of Division A - 1 way;
at least one of Divisions B and C - there will be one way when none will be there, so Total-1=2^2-1=3;
at least two of Divisions D, E, and F- none is there-1 way and one is there-3 ways, so total-(1+3)=2^3-4; and
at least two of Divisions G, H, J, and K- none is there-1 way and one is there-4 ways, so total-(1+3)=2^4-5;

total ways = $$1*3*(2^3-4)(2^4-5)=1*3*4*11=132$$
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Joined: 02 Aug 2009
Posts: 7671
Re: How many organizational structures can be formed that consist of Divis  [#permalink]

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26 Nov 2018, 07:34
chetan2u wrote:
kchen1994 wrote:
How many organizational structures can be formed that consist of Division A; at least one of Divisions B and C; at least two of Divisions D, E, and F; and at least two of Divisions G, H, J, and K?

a) 60
b) 90
c) 99
d) 120
e) 132

Hi ParthSanghavi,

The way would be to see how each set will turn out to be..
consist of Division A - 1 way;
at least one of Divisions B and C - there will be one way when none will be there, so Total-1=2^2-1=3;
at least two of Divisions D, E, and F- none is there-1 way and one is there-3 ways, so total-(1+3)=2^3-4; and
at least two of Divisions G, H, J, and K- none is there-1 way and one is there-4 ways, so total-(1+3)=2^4-5;

total ways = $$1*3*(2^3-4)(2^4-5)=1*3*4*11=132$$

Seems, Karishma has also replied in the meantime. Thanks
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Joined: 02 Oct 2017
Posts: 729
Re: How many organizational structures can be formed that consist of Divis  [#permalink]

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29 Nov 2018, 23:46
1
For this question one needs to manually calculate cases

1*(2C1+2C2)*(3C2+3C3)*(4C2+4C3+4C4)
=1*3*4*11
=132

Posted from my mobile device
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Re: How many organizational structures can be formed that consist of Divis   [#permalink] 29 Nov 2018, 23:46
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