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Difficulty:
95%
(hard)
Question Stats:
28% (03:16) correct
72%
(02:48)
wrong
based on 67
sessions
History
Date
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Result
Not Attempted Yet
A survey was performed on exchanging Christmas presents. Of the people surveyed, one eighth exchanged the most presents on December 24, five sixths exchanged the most on December 25, and 55 people exchanged the most on January 6. In addition, 22 percent of the people surveyed exchange presents on at least four days during Christmas. What is the smallest possible number of people surveyed?
A) 1,300
B) 1,320
C) 1,350
D) 1,400
E) 1,800
A) 1,300
B) 1,320
C) 1,350
D) 1,400
E) 1,800
nemoexplicabo
22 Apr 2026, 15:34
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- Let N be the total surveyed.
- Dec 24 is N/8 people, so N must be divisible by 8.
- Dec 25 is (5/6)N people, so N must be divisible by 6.
- That means N must be divisible by LCM(8,6) = 24.
- “Exactly 22%” means 11/50 of N. People counts must be whole, so N must also be divisible by 50. (I almost went full Venn diagram here the first time.)
- Combine: N must be divisible by LCM(24, 50) = 600.
- Jan 6 is exactly 55 people. Since 55 is less than 600, it doesn’t add any new constraint beyond N being at least 55.
- Scan the answer choices: 1,200 works since it’s a multiple of 600. 1,320 fails the /50 check (0.22*1320 = 290.4 people, nope). 1,400 fails the /6 check. 1,800 and 2,400 work but are bigger.
- Minimum possible is 1,200. Takeaway: whenever you see percentages of people, run the divisibility sanity check before doing anything fancy.
24 Apr 2026, 16:34
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55 is an important number in this question
