SOLUTION: The president just recently appointed 25 generals of the army, of these, 14 have already served in Gulf War, 12 in the cold war of Russia, and 10 in war in Syria. Therefore 4 who h

Question 1081543: The president just recently appointed 25 generals of the army, of these, 14 have already served in Gulf War, 12 in the cold war of Russia, and 10 in war in Syria. Therefore 4 who have served both in Gulf War and Syria, 6 served both in Gulf War and Russia, and 3 have served both Russia and Syria. How many generals who had served both Gulf War, Russia, and Syria.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Make a Venn diagram with 3 overlapping circles.
You should be able to count 7 distinct regions.
The region in the center is the generals who
served in G, R, and S. Call that region X.
G = 14
R = 12
S = 10
G AND R = 6
G AND S = 4
R AND S = 3
---------------
The trick now is to identify each of the 7 distinct regions
so that you have eliminated all the overlaps.
-----------------------------------------
A little shortcut is to lump together the 4 regions that make
up G. That gives you 14.
Then I get 2 more regions from R minus overlap with G
Then I get 1 more which is S and ONLY S ( no overlaps )
4 + 2 + 1 = 7
--------------------------
14 +
12 - 6
10 - 4 - ( 3-x )
This should add up to 25
---------------------------------
14 + 12 - 6 + 10 - 4 - 3 + x = 25
23 + x = 25
x = 2
That means there are 2 generals who seved in
Gulf War, Russia, and Syria.
----------------------------
Hope this helps. The key is to add up the 7 regions
without overlaps to find x
-----------------------------
Now you can check by adding up each of the 7
(1) 14 - 4 - ( 6-2 )
(2) 12 - 6 - ( 3-2 )
(3) 10 - 4 - ( 3-2 )
(4) 4 - 2
(5) 6 - 2
(6) 3 - 2
(7) 2
---------------------
Add them up
(1) 6
(2) 5
(3) 5
(4) 2
(5) 4
(6) 1
(7) 2
---------
25 total

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