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18 Nov 2025, 23:44
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D
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Difficulty:
35%
(medium)
Question Stats:
70% (01:35) correct
30%
(02:04)
wrong
based on 137
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In a certain rural town, 250 households contain a dog or a cat or both. How many of these households contain both a dog and a cat if 75 of 250 households do not contain a dog?
(1) 150 of the 250 households do not contain a cat.
(2) The total number of households that contain a cat is 100.
(1) 150 of the 250 households do not contain a cat.
(2) The total number of households that contain a cat is 100.
19 Nov 2025, 00:58
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Only cats = c
Only dogs = d
Both = b
75 of 250 households do not contain a dog => c = 75
c + d + b = 250 (as Neither = 0)
=> d + b = 250 - 75 = 175
(1) 150 of the 250 households do not contain a cat.
No cats = d = 150
Now d + b = 175
=> 150 + b = 175
=> b = 25
Sufficient
(2) The total number of households that contain a cat is 100.
c +b = 100
We know c = 75
=> b = 25
Sufficient
IMO Option D
Only dogs = d
Both = b
75 of 250 households do not contain a dog => c = 75
c + d + b = 250 (as Neither = 0)
=> d + b = 250 - 75 = 175
(1) 150 of the 250 households do not contain a cat.
No cats = d = 150
Now d + b = 175
=> 150 + b = 175
=> b = 25
Sufficient
(2) The total number of households that contain a cat is 100.
c +b = 100
We know c = 75
=> b = 25
Sufficient
IMO Option D
Bunuel
19 Nov 2025, 10:40
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from question Union value of houses with dogs and cats =250
total no of houses with dogs =250-houses without dogs=175
so to find the houses with both dogs and cats i.e. intersection value, we must know the houses with no of cats, which can be easily find out from 1. as 250-150=100 and in 2. exclusively given
hence both statements are individually sufficient.
D
total no of houses with dogs =250-houses without dogs=175
so to find the houses with both dogs and cats i.e. intersection value, we must know the houses with no of cats, which can be easily find out from 1. as 250-150=100 and in 2. exclusively given
hence both statements are individually sufficient.
D
