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31 Dec 2023, 08:34
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At an office Christmas party, where at least one person likes eggnog and at least one likes cocoa, is the number of people who like eggnog at least three times the number of those who like cocoa?
(1) The number of attendees who neither like eggnog nor cocoa is twice the number of those who like eggnog.
(2) The number of attendees who like either eggnog or cocoa, or both, is four times the number of those who like cocoa.
(1) The number of attendees who neither like eggnog nor cocoa is twice the number of those who like eggnog.
(2) The number of attendees who like either eggnog or cocoa, or both, is four times the number of those who like cocoa.
31 Dec 2023, 08:34
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Official Solution:
At an office Christmas party, where at least one person likes eggnog and at least one likes cocoa, is the number of people who like eggnog at least three times the number of those who like cocoa?
The question asks whether {Eggnog} ≥ 3*{Cocoa}, given that both {Eggnog} and {Cocoa} are more than 0.
(1) The number of attendees who neither like eggnog nor cocoa is twice the number of those who like eggnog.
This implies that {Neither} = 2*{Eggnog}, which doesn't help us conclude whether {Eggnog} ≥ 3*{Cocoa}. Not sufficient.
(2) The number of attendees who like either eggnog or cocoa, or both, is four times the number of those who like cocoa.
This implies that {Eggnog} + {Cocoa} - {Both} = 4*{Cocoa}, which simplifies to {Eggnog} = 3*{Cocoa} + {Both}. Since {Both} cannot be negative, it means that {Eggnog} is always at least 3*{Cocoa}. Sufficient.
Answer: B
At an office Christmas party, where at least one person likes eggnog and at least one likes cocoa, is the number of people who like eggnog at least three times the number of those who like cocoa?
The question asks whether {Eggnog} ≥ 3*{Cocoa}, given that both {Eggnog} and {Cocoa} are more than 0.
(1) The number of attendees who neither like eggnog nor cocoa is twice the number of those who like eggnog.
This implies that {Neither} = 2*{Eggnog}, which doesn't help us conclude whether {Eggnog} ≥ 3*{Cocoa}. Not sufficient.
(2) The number of attendees who like either eggnog or cocoa, or both, is four times the number of those who like cocoa.
This implies that {Eggnog} + {Cocoa} - {Both} = 4*{Cocoa}, which simplifies to {Eggnog} = 3*{Cocoa} + {Both}. Since {Both} cannot be negative, it means that {Eggnog} is always at least 3*{Cocoa}. Sufficient.
Answer: B
02 Aug 2024, 14:11
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Question, if there is atleast one who like eggnog and atleast one who likes cocoa, shouldn’t the people who like neither be 0.
And by this logic if we check statement one, there is no one who likes cocoa. Since those like cocoa is three times the number who like neither. Which should again be 0, as at least one like cocoa or atleast one like eggnog as per question seen.
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And by this logic if we check statement one, there is no one who likes cocoa. Since those like cocoa is three times the number who like neither. Which should again be 0, as at least one like cocoa or atleast one like eggnog as per question seen.
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