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29 Aug 2006, 05:16
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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.
(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.
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29 Aug 2006, 13:53
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Lets say the three sets are S, O and P.
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.
MG
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.
MG
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
