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How many organizational structures can be formed that consist of Divis

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

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New post 18 Nov 2018, 18:18
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Question Stats:

43% (02:19) correct 57% (01:49) wrong based on 53 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
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Re: How many organizational structures can be formed that consist of Divis  [#permalink]

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New post 26 Nov 2018, 06:21
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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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Re: How many organizational structures can be formed that consist of Divis  [#permalink]

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New post 26 Nov 2018, 06:26
VeritasKarishma 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


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
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Re: How many organizational structures can be formed that consist of Divis  [#permalink]

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New post 26 Nov 2018, 06:32
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 = \(1*3*(2^3-4)(2^4-5)=1*3*4*11=132\)
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: How many organizational structures can be formed that consist of Divis  [#permalink]

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New post 26 Nov 2018, 06:34
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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: How many organizational structures can be formed that consist of Divis  [#permalink]

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New post 29 Nov 2018, 22:46
For this question one needs to manually calculate cases

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

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Re: How many organizational structures can be formed that consist of Divis &nbs [#permalink] 29 Nov 2018, 22:46
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