Question 1199476
This problem is solved using Venn diagrams.  I will break down the problem step by step and sentence by sentence as shown below.
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The total number of students who take Geotechnical (g) only, Theory (t) only, and Hydraulics (h) only is 12.
---> E1:  g + t + h = 12
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The total number of students who take Hydraulics (h) only is twice the number of students who take Geotechnical (g) only.  
---> E2:          h = 2g
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The number of students who take Theory (t) only is thrice the number of students who take Geotechnical (g) only.  
---> E3:          t = 3g
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Substituting “3g” for “t”, and “2g” for “h” in equation E1, we have:  g + 3g + 2g = 12 = 6g.  
Thus, from Equation E1, g = 2.  From equation E2, h = 4.  From equation E3, t = 6.
|  See the Venn diagram picture for reference.
The number of students who take Theory, Geotechnical, and Hydraulics is 3.
This is the total number of students in the innermost region of our diagram.  Next, we work our way out.
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The number of students who take Theory and Geotechnical is 5.
Let x = the number of students who take Theory and Geotechnical, but not Hydraulics.
Then, we have:  x + 3 = 5.  Thus, x = 2.
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The number of students who take Theory and Hydraulics is 8.
Let z = the number of students who take Theory and Hydraulics, but not Geotechnical.
Then, we have:  z + 3 = 8.  Thus, z = 5.
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The number of students who take Geotechnical and Hydraulics is 7.
Let y = the number of students who take Geotechnical and Hydraulics, but not Theory.
Then, we have:  y + 3 = 7.  Thus y = 4.
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Therefore, the total number of students who take Hydraulics = y + 3 + z + h = 4 + 3 + 5 + 4 = 16.