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18 Dec 2025, 09:00
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At least one: 150
Both: 95
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
58% (02:25) correct
42%
(02:31)
wrong
based on 210
sessions
History
Date
Time
Result
Not Attempted Yet
12 Days of Christmas Competition
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In a recent neighborhood survey, fewer than 170 households were surveyed regarding pet ownership. Of those, 150 households reported owning a dog, while 95 households reported owning a cat.
In the table, select for At least one the number of households that own at least one of a dog or a cat, and select for Both the number of households that own both a dog and a cat that would be jointly consistent with the given information. Make only two selections, one in each column.
I31-20
| At least one | Both | |
| 65 | ||
| 75 | ||
| 95 | ||
| 150 | ||
| 160 | ||
| 170 |
ShowHide Answer
Official Answer
At least one: 150
Both: 95
18 Dec 2025, 10:00
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Bunuel
GMAT Club Official Explanation:
Given that 150 households own a dog and 95 own a cat, we have:
At least one = 150 + 95 - Both = 245 - Both.
Thus, we need two options for At least one (245 - Both) and Both, such that their sum is 245.
From the options, two pairs satisfy this condition for (At least one, Both): (170, 75) and (150, 95). However, since fewer than 170 households were surveyed, At least one cannot be 170. Therefore, the only valid pair is (At least one, Both) = (150, 95).
General Discussion
18 Dec 2025, 09:27
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Let the no. owning both be x
Household owning 1 dog or cat = 150-5-x = 245-x
Since surveyed < 170, therefore, 245-x<170
x<75
Also, No. owning both<(or equal to) no. owning Cat
only value satisfies is x=95
And atleast 1 = 245-95 = 150
Hence, Both = 95 & Atleast 1 =150
Household owning 1 dog or cat = 150-5-x = 245-x
Since surveyed < 170, therefore, 245-x<170
x<75
Also, No. owning both<(or equal to) no. owning Cat
only value satisfies is x=95
And atleast 1 = 245-95 = 150
Hence, Both = 95 & Atleast 1 =150
