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Law firm has branches in X, Y, Z states. Each lawyer has either a lice

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Law firm has branches in X, Y, Z states. Each lawyer has either a lice  [#permalink]

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New post Updated on: 20 May 2020, 00:02
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Law firm has branches in X, Y, Z states. Each lawyer has either a license in one state or in all three states. There are 10, 11, 13 lawyers licensed in the 3 states respectively, and 28 lawyers in total in the firm. How many lawyers are only licensed in state Z?

A. 2
B. 4
C. 6
D. 8
E. 10

Originally posted by cnsih1532 on 19 May 2020, 23:46.
Last edited by cnsih1532 on 20 May 2020, 00:02, edited 1 time in total.
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Re: Law firm has branches in X, Y, Z states. Each lawyer has either a lice  [#permalink]

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New post 20 May 2020, 00:01
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cnsih1532 wrote:
Law firm has branches in X, Y, Z states. Each lawyer has either a license in one state or in all three states. There are 10, 11, 13 lawyers licensed in the 3 states respectively, and 28 lawyers in total in the firm. How many lawyers are only licensed in state Z?

A. 2
B. 4
C. 6
D. 8
E. 10



SO we have only 2 categories, either all 3 or any 1.
When we add , 10, 11 and 13, we are adding the number of lawyers who are in all three THREE times.

Therefore, if the number of lawyers licensed in all three states is x, the total is (10-x)+(11-x)+(13-x)+x=28
34-2x=28...x=3.

So 13-3 or 10 lawyers are only licensed in state Z.
Similarly for X, Y and Z, the numbers are 7, 8, and 10 respectively, and 3 in all three states.

E

OA is wrong
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Re: Law firm has branches in X, Y, Z states. Each lawyer has either a lice  [#permalink]

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New post 26 May 2020, 06:30
cnsih1532 wrote:
Law firm has branches in X, Y, Z states. Each lawyer has either a license in one state or in all three states. There are 10, 11, 13 lawyers licensed in the 3 states respectively, and 28 lawyers in total in the firm. How many lawyers are only licensed in state Z?

A. 2
B. 4
C. 6
D. 8
E. 10


total branches ; 3 ( x,y,z)
each lawyer has (all three or in 1 state)
given total 28 lawyers in firm
so let each state license be x
we have 10-x+11-x+13-x+x =28
solve for 2x = 34-28 ; 6 ; x = 3
so state z has 13-3 ; 10 lawyers
OPTION E
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Re: Law firm has branches in X, Y, Z states. Each lawyer has either a lice  [#permalink]

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New post 30 May 2020, 14:05
cnsih1532 wrote:
Law firm has branches in X, Y, Z states. Each lawyer has either a license in one state or in all three states. There are 10, 11, 13 lawyers licensed in the 3 states respectively, and 28 lawyers in total in the firm. How many lawyers are only licensed in state Z?

A. 2
B. 4
C. 6
D. 8
E. 10


Total = 28
X + Y +Z = 34
So, (34-28)= 6 . Since, total = separate - both - 2(all three) + neither. 28 = 34 -(2*3). so 3 lawyers have license in all states. Lawyers licensed only in state Z (13-3)=10
E is the answer
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Re: Law firm has branches in X, Y, Z states. Each lawyer has either a lice   [#permalink] 30 May 2020, 14:05

Law firm has branches in X, Y, Z states. Each lawyer has either a lice

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