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Ham and Roast Beef


A total of $418$ ham and roast beef sandwiches were ordered at a restaurant over the course of two days. The manager made a report detailing exactly the number of each type of sandwich ordered.

Unfortunately, the report was damaged, and only the following details are known: $209$ orders were for ham with cheese, $177$ orders were for roast beef (some with cheese, and some without cheese), and a total of $122$ orders altogether were for sandwiches without cheese.

Which of the following is a correct conclusion based on the known data?



Sandwiches containing ham were ordered more than twice as often as those containing roast beef.


More than half of all of the roast beef sandwiches ordered were ordered "without cheese".


Half of the sandwiches ordered contained ham.


Over $100$ roast beef sandwiches with cheese were ordered.