Question: A survey was conducted among 1000 people to know about their eating habits. It was found that 3/5 of the people prefer homemade food and rest prefer eating outside, 1/4th of the people who prefer eating outside like continental. If in total there were 650 people who do not like continental, how many people who prefer homemade food do not like continental?
- 250
- 300
- 350
- 400
- None of these
“A survey was conducted among 1000 people to know about their eating habits.”- 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 number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
As per the question, we see that 2/5 x 1000 = 400 people prefer eating outside
Among these 400 people, 1/4 x 400 = 100 people like continental.
Since 650 people do not like continental, 1000 - 650 = 350 people like continental.
We can see from the problem statement that 3/5 x 1000 = 600 people prefer homemade food.
Since 350 - 100 = 250 of these 600 people like continental,
600 - 250 = 350 of these people don’t like continental.
Alternatively, since 100 of 400 people who prefer eating outside like continental,
400 - 100 = 300 people who prefer eating outside do not like continental.
Since the total number of people who don’t like continental is 650, it must be true that 650 - 300 = 350 people who prefer homemade food don’t like continental.
Correct Answer: C
Approach Solution 2:
Total: 1000 people
=> ⅗ of the people prefer homemade food:
= ⅗ * 1000 = 600
=> Rest prefer eating outside: 1000 - 600 = 400
=> ¼ of the people who prefer eating outside like continental:
=> ¼ * 400 = 100
=> People eating outside but do not like continental: 400-100 = 300.
If in total there were 650 people who do not like continental, then people who prefer homemade food but do not like continental are 650 - 300 = 350.
Correct Answer: C
Approach Solution 3:
We can observe from the question that 2/5 of 1000 individuals, or 400 people, prefer to eat outside.
100 of these 400 people—or 1/4 of them—like continental food.
Since 650 individuals dislike continental, 350 individuals favour continental (1 000 - 650).
The problem statement indicates that 3/5 x 1000 = 600 individuals favour homemade cuisine.
Since 250 of these 600 people—350 out of the total—like continental food, 350 of them—600 out of the total—do not.
On the other hand, because 100 out of 400 individuals who enjoy dining outside like continental food, 400 - 100 = 300 people who prefer eating outside do not.
Since there are 650 individuals who dislike continental food overall, it follows that 350 people who favour homemade food dislike continental.
Correct Answer: C
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