What percentage of families in the state have annual incomes over $50,000 and have a net worth over $500,000? (1) 65% of all the families in the state have an annual income over $50,000. (2) 20% of the families in the state with an annual income over $50,000 have a net worth above $500,000.

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. Either statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(C) Statement (1) alone is not sufficient, because it only gives us the percentage of families in the state with the required annual income, but gives no information regarding the net worth. Statement (2) is not sufficient because, although it tells you about the percentage of families that satisfy the question, it does not give you the percentage of families in the state that have an annual income of $50,000. Statements (1) and (2) COMBINED are sufficient. 20% of the 65% are families who both have annual incomes over $50,000 AND have a net worth above $500,000. To find out the percentage of people with both traits, multiply the two independent variables. The two statements give these two variables. Remember, however, that for these questions you do not need to solve for an answer; you simply need to establish whether or not you have sufficient information to do so. ---------- What about people who earn less than 50,000 but have net worth above 500,000, as per inheritance?

The question does NOT ask to calculate those. But if it did, there would NOT be enough information to calculate. We would be able to calculate the percentage of the families that had an annual income NOT more than $50,000 using the first statement, 100% – 65% = 35%. But we would NOT know what percentage of such families had an income more than $500,000. There is NO such information in the statements.

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