JEE Main 2015 · 10 Apr · Shift 1 · Mathematics Q61

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MathematicsSingle correct+4 / -1Question 61 of 90

In a certain town, 25% of the families own a phone and 15% own a car ; 65% families own neither a phone nor a car and 2,000 families own both a car and a phone. Consider the following three statements :

(a) 5% families own both a car and a phone.

(b) 35% families own either a car or a phone.

Then,

Only (a) and (b) are correct.

Only (a) and (c) are correct.

Only (b) and (c) are correct.

All (a), (b) and (c) are correct.

Answer and worked solution

Official answer: D

$P(\text{phone}\cup\text{car})=100-65=35\%$ , so $P(\text{both})=25+15-35=5\%$ . Then 2000 families are 5%, giving 40,000 families. All three statements are correct.

Topics:Sets and operations

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JEE Main 2015 · 10 Apr · Shift 1, Mathematics question 61