ISI2018-DCG-13

Question

In a certain town, $20\%$ families own a car, $90\%$ own a phone, $5 \%$ own neither a car nor a phone and $30, 000$ families own both a car and a phone. Consider the following statements in this regard:

1. $10 \%$ families own both a car and a phone.
2. $95 \%$ families own either a car or a phone.
3. $2, 00, 000$ families live in the town.

Then which one of the following is true?

• A. (i) & (ii) are correct and (iii) is wrong.
• B. (i) & (iii) are correct and (ii) is wrong.
• C. (ii) & (iii) are correct and (i) is wrong.
• D. (i), (ii) & (iii) are correct.

Answer 1

Answer is option C (i) is wrong because 15% families own both a car and a phone not 10% total 200000 families are there. Let number of families be n so families that own only car is 0.2n-30,000 and families that own phone are 0.9n-30,000 so 0.2n-30,000+0.9n-30,000+30,000+0.05n=n solving that we get n=200000.

now there are 30,000 families that own a car and phone so 30,000*100/200000=15% there 10,000 families that own a car and 180000 families that own a phone so 10,000+180000=190000 that own a car or phone so it is 95% of families.

Comments

Calculation part?

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0.2n-30,000+0.9n-30,000+30,000+0.05n=n

plz explain the highlight part???

@Yash4444

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Draw venn diagram and try to understand let A be then families having car B be the families having phone so families having only car is 0.2n-(A∩B) and families having only phone be 0.9n-(A∩B) and A ∩B is given 30,000 so 0.2n-30,000+0.9n-30,000 Draw venn diagram you will get clear idea

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only car=0.2n-30,000 only phone =0.9n-30,000 both car and phone=30,000 neither car nor phone 0.5n so only car+only phone+both car and phone + neither car and phone gives me total number of families therefore 0.2n-30,000+0.9n-30,000+30,000+0.05n using venn diagram .

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Ok ....i got it thanks