In a town 25% families own a phone and 15% own a car. 65% families own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard: I. > 10% families own both a car and a phone. II. > 35% families

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Q: 135 (IAS/1999)
In a town 25% families own a phone and 15% own a car. 65% families own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard:
I. 10% families own both a car and a phone.
II. 35% families own either a car or a phone.
III. 40,000 families live in the town.
Which of the above statements are correct ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,5,3,1,1,5,1

keywords: 

{'families': [2, 1, 2, 2], 'car': [0, 2, 12, 17]}

In option 1, the first part is correct because 2000 families own both car and phone which should be >10% of total families. However, the second part is incorrect as it is stated that 65% families own neither a car nor a phone. So rest 35% families own either a car or a phone which is not >35%.

In option 2, again the first part (I) is correct, but the second part (III) is difficult to ascertain without knowing exact number of families in town.

For option 3, the first part (II) is correct as mentioned above. If 2000 families represent more than 10%, then the total number of families in town must be <20,000 (because 2000 is 10% of 20,000), therefore the second part (III) is also correct.

Option 4 is invalid as option 1 and 2 are partially incorrect.

Hence, considering all points, option 3 (II and III) are the correct statements.

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