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Each of 200 large companies was asked whether it employed a [#permalink]
29 Aug 2006, 04:16
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Each of 200 large companies was asked whether it employed a safety officer, an ombudsman, or a staff psychologist. 40 companies did not employ any of the three, while there were twice as many companies with a safety officer as there were with an ombudsman. The survey also found that there were three times as many companies with a staff psychologist as there were without one. Did more than 5 companies have an ombudsman and a safety officer but not a staff psychologist?
(1) 6 companies had an ombudsman, but neither a safety officer nor a staff psychologist.
(2) Each company that had a safety officer had either an ombudsman or a staff psychologist, and 6 companies had all three.
Given that P = 3P' (since number that have psychologists are three times those that don't have psychologists)
Also P + P' = 200. (every set + its complement is the total sum)
Therefore P' = 50.
and P = 150.
Now the total within the sets is actually only 160, since 40 companies have none of the three.
Therefore thinking of a venn diagram and excluding P, (S only) + (O only ) + (O intersection S only) = 10.
A. says that of these (O only) = 6. Therefore O intersection S only (which is the question) must be 4 or less.
thus, A is sufficient... can't wrap my head around B yet, so answer should be A or D.
My problem is for this solution I am not able to use one of the specified critieria (S = 2 * O) - perhaps it comes into use in the second part.