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 Math Help > Math Puzzles > 2004 State Logic Quiz > Question 10 > Question 10

# Academic Decathlon 2004 State Championship Logic Quiz

## Question 10

The army is training its soldiers in one or more skills, depending on their aptitude.  This Venn Diagram shows how many soldiers are trained in each of three skills:

Using the diagram, above, answer these questions:

a. How many soldiers have been trained in Rocket Launching or Field Combat?

b. How many soldiers have been trained as Scouts and Field Combat but not in Rocket Launching?

c. How many soldiers have not been trained in Field Combat?

d. What percentage of soldiers can be used as scouts?  (Round to the nearest full percentage)

e. If 20 of those trained in Scouting and Rocket Launching are on leave, how many are left on base who can Scout or Launch Rockets?

f. How many can Scout or do Field Combat but haven't been trained to Launch Rockets?

a. How many soldiers have been trained in Rocket Launching or Field Combat?  339.

The total number of soldiers is 64 + 45 + 78 + 60 + 12 + 30 + 114 = 403.  Of these 403 soldiers, just 64 were trained in Scouting alone.  These are the only soldiers who were not trained in Rocket Launching or Field Combat, so the answer is 403-64=339.

b. How many soldiers have been trained as Scouts and Field Combat but not in Rocket Launching?  60.

The Venn diagram shows that 60 soldiers were trained as Scouts and Field Combat but not Rocket Launching.

c. How many soldiers have not been trained in Field Combat?  187.

64 + 45 + 78 = 187.  These are the numbers in the Venn diagram that fall outside the Field Combat circle.

d. What percentage of soldiers can be used as scouts?  (Round to the nearest full percentage)  45%

64 + 45 + 60 + 12 = 181 soldiers trained as scouts.  181/403 = 45% (to the nearest full percentage).

e. If 20 of those trained in Scouting and Rocket Launching are on leave, how many are left on base who can Scout or Launch Rockets?  269.

The number trained in Scouting or Launching Rockets is 403 - 114 = 289.  If 20 of them are on leave, then 269 remain.

f. How many can Scout or do Field Combat but haven't been trained to Launch Rockets?  238.

64 + 60 + 114 = 238

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