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22 Jan 2022, 11:24
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C
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Difficulty:
45%
(medium)
Question Stats:
72% (01:51) correct
28%
(02:05)
wrong
based on 1413
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A certain firm has 28 lawyers in three states. These lawyers have license either in only one state or all three states. If 10 have license in state X, 11 have license in Y, 13 have license in Z. How many lawyers have license only in state Z ?
A. 3
B. 6
C. 10
D. 11
E. 13
A. 3
B. 6
C. 10
D. 11
E. 13
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yashikaaggarwal
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Joined: 19 Jan 2020
Last visit: 10 Aug 2026
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22 Jan 2022, 12:43
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Total => 28 (A+B+C+D) ----------(1)
These lawyers have license either in only one state or all three states. If 10 have license in state X, 11 have license in Y, 13 have license in Z.
A+D = 10
B+D = 11
C+D = 13
Adding all 3
A+B+C+3D = 34 ------------(2)
Subtracting equation 1 from equation 2
A+B+C+3D = 34
A+B+C+D = 28
----------------
2D = 6 => D = 3
Now to get only C
C+D = 13
C = 13-3 => 10
Answer is C
Posted from my mobile device
These lawyers have license either in only one state or all three states. If 10 have license in state X, 11 have license in Y, 13 have license in Z.
A+D = 10
B+D = 11
C+D = 13
Adding all 3
A+B+C+3D = 34 ------------(2)
Subtracting equation 1 from equation 2
A+B+C+3D = 34
A+B+C+D = 28
----------------
2D = 6 => D = 3
Now to get only C
C+D = 13
C = 13-3 => 10
Answer is C
Posted from my mobile device
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31 Mar 2024, 02:42
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zaprico
Because each of AnB, AnC, and BnC also includes AnBnC, and thus the sum of AnB + AnC + BnC won't be 0. You should use the second formula for three overlapping sets:
\(Total = A + B + C - (sum \ of \ EXACTLY \ 2-group \ overlaps) - 2*(all \ three) + Neither\).
28 = 10 + 11 + 13 - 0 - 2*(all three) + 0
(all three) = 3
Only Z = Z - (all three) = 13 - 3 = 10.
Answer: C.
For further insights into the distinctions between these two formulas, check out ADVANCED OVERLAPPING SETS PROBLEMS.
Hope it helps.
