Question: A market survey showed that 76 percent of the visitors at a certain resort came from Pacific or southwestern states. Of these,\(2\over3\)were from California, and 87 percent of the Californians were from southern California. Approximately what percent of the visitors at the resort were from southern California?

1. 40%
2. 45%
3. 50%
4. 55%
5. 65%

Answer:
Approach Solution (1):
Given: A market survey showed that 76 percent of the visitors at a certain resort came from Pacific or southwestern states
Of these,\(2\over3\)were from California, and 87 percent of the Californians were from southern California
To find: The approximate percent of the visitors at the resort who were from southern California
Approach and Working:
If we assume the total visitors to be 100
Visitors from Pacific or southern states = 76% of 100 = 76
Visitors from California =\(76*{2\over3}=50(approx)\)
Visitors from the southern California = 87% of 50 = 43.5 = approximately 45
Correct option: B

Approach Solution (2):
Let the total population be 100
So, 76 visitors came from Pacific or southwestern states
Out of the 76 visitors 50.67 (i.e.\(2\over3\)of 76) visitors came from California
Again out of those 50.67 visitors 44.08 (87% of 50.67) visitors came from southern California
So, we have approximately 45% visitors who came from southern California
Correct option: B

Approach Solution (3):
76% =\({3\over4}(+)\)
87% =\(7\over8\)
Now
\({3\over4}*{2\over3}*{7\over8}={14\over32}={7\over16}\)
\({7\over16}=43\%(+)\)
Correct option: B

“A market survey showed that 76 percent of the visitors at a certain resort came from Pacific or southwestern states. Of these,\(2\over3\)were from California, and 87 percent of the Californians were from southern California. Approximately what percent of the visitors at the resort were from southern California?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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