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GMAT Percentage (Data Sufficiency)
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Author:  questioner [ Tue Jul 27, 2010 4:45 am ]
Post subject:  GMAT Percentage (Data Sufficiency)

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.
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I am confused by the wording of the question.
Should not statement 2 be sufficient here since it satisfies both requirements?

Author:  Gennadiy [ Tue Jul 27, 2010 5:30 am ]
Post subject:  Re: math (test 5, question 7): data sufficiency, percentages

Looking at Venn diagram when solving this question may help you to understand it better.


That is what we know when use statement (2) by itself:


Note that we know only that families in the state that have annual incomes over $50,000 and have a net worth over $500,000 (painted in dark) make 20% of the families in the state with an annual income over $50,000. But what percentage does it make out of total? We do not know, because we do not know what percentage out of total make families with an annual income over $50,000. Is 100%, or 50% or anything else?


But when we use statement (1) together with statement (2) we can answer the question:


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