12 Days of Christmas GMAT Competition - Day 8: At an office Christmas

Question

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.

Bunuel · Accepted Answer

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.

Kinshook · Answer

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?

Eggnog  ~Eggnog  Total  
  Cocoa  x  y  x+y  
  ~Cocoa  z  w  z+w  
  Total  x+z  y+w  x+y+z+w  
 
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.
 
    Eggnog  ~Eggnog  Total  
  Cocoa  x  y  x+y  
  ~Cocoa  z  w  z+w  
  Total  x+z  y+w  x+y+z+w  
 
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.
 
    Eggnog  ~Eggnog  Total  
  Cocoa  x  y  x+y  
  ~Cocoa  z  w  z+w  
  Total  x+z  y+w  x+y+z+w  
 
x + y + z = 4 (x+y)
z = 3(x+y) = 3x + 3y > 2x +3y since x>=0
SUFFICIENT

IMO B

Oppenheimer1945 · Answer

Is A+C>3(B+C)
 Or Is A>3B+2C

S1) D=2A+2C
Not Suff

S2)A+B+C=4B+4C
=> A=3B+3C clearly C>0 we can say 
A>3B+2C (Suff)

B)

missionmba2025 · Answer

Your analysis is correct.

Statement 1 is insufficient to determine whether the number of people who like eggnog is at least three times the number of those who like cocoa. It only provides information about the relationship between those who like neither drink and those who like eggnog, but it doesn't give any direct comparison between eggnog and cocoa preferences.

Statement 2 is sufficient to determine that the number of people who like eggnog is at least three times the number of those who like cocoa. Here's a breakdown of the logic:

Equation from Statement 2: a + b + c = 4(b + c)
Simplifying: a = 3(b + c)
Adding b to both sides: a + b = 3(b + c) + b
Interpretation:
a + b represents the total number of people who like eggnog (either only eggnog or both drinks).
b + c represents the total number of people who like cocoa (either only cocoa or both drinks).
Conclusion: The equation a + b = 3(b + c) + b shows that the number of people who like eggnog (a + b) is at least three times the number of people who like cocoa (b + c), with the possibility of being even more due to the additional "b" term.
Therefore, the answer is B: Statement 2 alone is sufficient.

IMO B

Catman · Answer

Let persons who like only eggnog = e
Let persons who like both eggnog and cocoa = b
Let persons who like only cocoa = c
Not like anything = n

Total persons in the party = a+b+c+n
Persons who like eggnog = e+b
Persons whol like Cocoa = c+b

(1) The number of attendees who neither like eggnog nor cocoa is twice the number of those who like eggnog. 
n= 2(e+b)
From this we cannot establish any relation between Cocoa and eggnog. Insufficient.

(2) The number of attendees who like either eggnog or cocoa, or both, is four times the number of those who like cocoa. 
Number of attendees who like either eggnog or cocoa or both = e+b+c 
Number of persons who like cocoa = b+c
e+b+c = 4(b+c)
e= 3(b+c)
The person who likes only eggnog is three times the person who like cocoa.
Adding 'b' on both sides we get
e+b = 3(b+c) +b

Number of Person Who likes eggnog is atleast three times the the number of those who like cocoa when b=0 e =3c

Sufficient

IMO B.

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12 Days of Christmas GMAT Competition - Day 8: At an office Christmas

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