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20 Dec 2023, 07:00
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B
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Difficulty:
65%
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Question Stats:
60% (02:27) correct
40%
(02:29)
wrong
based on 245
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12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun
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.
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.
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21 Dec 2023, 05:01
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GMAT Club Official Explanation:
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.
General Discussion
20 Dec 2023, 07:53
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Asked: 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?
x+z> 0
x+y>0
Is x + z > 3(x+y) ?
Is z > 2x + 3y ?
(1) The number of attendees who neither like eggnog nor cocoa is twice the number of those who like eggnog.
z+w = 2(x+z)
w = 2x + z; z = w-2x
Relationship between z and (2x+3y) could not be established.
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.
x + y + z = 4 (x+y)
z = 3(x+y) = 3x + 3y > 2x +3y since x>=0
SUFFICIENT
IMO B
| Eggnog | ~Eggnog | Total | |
| Cocoa | x | y | x+y |
| ~Cocoa | z | w | z+w |
| Total | x+z | y+w | x+y+z+w |
x+y>0
Is x + z > 3(x+y) ?
Is z > 2x + 3y ?
(1) The number of attendees who neither like eggnog nor cocoa is twice the number of those who like eggnog.
| Eggnog | ~Eggnog | Total | |
| Cocoa | x | y | x+y |
| ~Cocoa | z | w | z+w |
| Total | x+z | y+w | x+y+z+w |
w = 2x + z; z = w-2x
Relationship between z and (2x+3y) could not be established.
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.
| Eggnog | ~Eggnog | Total | |
| Cocoa | x | y | x+y |
| ~Cocoa | z | w | z+w |
| Total | x+z | y+w | x+y+z+w |
z = 3(x+y) = 3x + 3y > 2x +3y since x>=0
SUFFICIENT
IMO B
