Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND EditionLast year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets. How many of the businesses did not report a net profit nor invest in foreign markets last year?
(1) Last year 12 of the 30 businesses reported a net profit and had investments in foreign markets.
(2) Last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both.
The
Double Matrix Method can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of businesses, and the two characteristics are:
- had a net profit or didn't have a net profit
- invested in foreign markets or didn't invest in foreign markets
So, we can set up our diagram as follows:
Now, if there are 30 businesses and 21 reported a net profit, then 9 did NOT report a net profit.
Similarly, if there are 30 businesses and 15 had investments in foreign markets, then 15 did NOT have investments in foreign markets. So, we can add that information to the diagram.
Note: I placed a star in the bottom right box to remind me that this is the value we are trying to determine.
Statement 1: Last year 12 of the 30 businesses reported a net profit and had investments in foreign markets. When we add this information to our diagram, we get the following:
Since we know the sums of the rows and columns, we can determine the values in every box to get the following:
Notice that we can determine the value for the bottom right box, which means we can answer the
target question with certainty.
So, statement 1 is SUFFICIENT
Statement 2: last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both. The three shaded boxes below represent the businesses that reported a net profit or invested in foreign markets, or both.
Since all 4 boxes must add to 30, we can see last remaining box must contain the 6 remaining businesses.
So, we can determine the value for the bottom right box, which means statement 2 is SUFFICIENT
Answer: D
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