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29 Apr 2025, 06:51
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
63% (02:22) correct
37%
(02:23)
wrong
based on 123
sessions
History
Date
Time
Result
Not Attempted Yet
At a certain company event, the snack table offered only sandwiches and salads. If 300 employees attended the event and 180 employees ate sandwiches, how many employees ate neither sandwiches nor salads?
(1) The number of employees who ate salads was equal to the number who ate neither sandwiches nor salads.
(2) The number of employees who ate only salads was equal to the number who ate both sandwiches and salads.
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
(1) The number of employees who ate salads was equal to the number who ate neither sandwiches nor salads.
(2) The number of employees who ate only salads was equal to the number who ate both sandwiches and salads.
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
10 May 2025, 04:45
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Official Solution:
At a certain company event, the snack table offered only sandwiches and salads. If 300 employees attended the event and 180 employees ate sandwiches, how many employees ate neither sandwiches nor salads?
{Total} = {Sandwiches} + {Salads} - {Both} + {Neither}
300 = 180 + {Salads} - {Both} + {Neither}
{Neither} = ?
(1) The number of employees who ate salads was equal to the number who ate neither sandwiches nor salads.
This implies {Salads} = {Neither}.
Substituting into the main equation:
300 = 180 + {Neither} - {Both} + {Neither}
300 = 180 + 2{Neither} - {Both}
We have two unknowns ({Neither} and {Both}). Cannot solve. Not sufficient.
(2) The number of employees who ate only salads was equal to the number who ate both sandwiches and salads.
This implies {Salads} - {Both} = {Both}, thus {Salads} = 2{Both}.
Substituting into the main equation:
300 = 180 + 2{Both} - {Both} + {Neither}
300 = 180 + {Both} + {Neither}
Again, two unknowns ({Both} and {Neither}). Cannot solve. Not sufficient.
(1)+(2) From (1), we have 300 = 180 + 2{Neither} - {Both}. From (2), we have 300 = 180 + {Both} + {Neither}. Thus, we have two distinct linear equations with two unknowns ({Neither} and {Both}), and we can solve for {Neither}. Sufficient.
Answer: C
At a certain company event, the snack table offered only sandwiches and salads. If 300 employees attended the event and 180 employees ate sandwiches, how many employees ate neither sandwiches nor salads?
{Total} = {Sandwiches} + {Salads} - {Both} + {Neither}
300 = 180 + {Salads} - {Both} + {Neither}
{Neither} = ?
(1) The number of employees who ate salads was equal to the number who ate neither sandwiches nor salads.
This implies {Salads} = {Neither}.
Substituting into the main equation:
300 = 180 + {Neither} - {Both} + {Neither}
300 = 180 + 2{Neither} - {Both}
We have two unknowns ({Neither} and {Both}). Cannot solve. Not sufficient.
(2) The number of employees who ate only salads was equal to the number who ate both sandwiches and salads.
This implies {Salads} - {Both} = {Both}, thus {Salads} = 2{Both}.
Substituting into the main equation:
300 = 180 + 2{Both} - {Both} + {Neither}
300 = 180 + {Both} + {Neither}
Again, two unknowns ({Both} and {Neither}). Cannot solve. Not sufficient.
(1)+(2) From (1), we have 300 = 180 + 2{Neither} - {Both}. From (2), we have 300 = 180 + {Both} + {Neither}. Thus, we have two distinct linear equations with two unknowns ({Neither} and {Both}), and we can solve for {Neither}. Sufficient.
Answer: C
General Discussion
10 May 2025, 02:55
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answer is C
Total people= no. ppl of eating salads + no. ppl of eating no. of sandwiches + no. ppl of eating neither + no. ppl of eating both
given data and taking q,n,b as variables
300 = 180 +q + n +b, find "n"
120= q+n+b
n=120-q-b
St1) n= q, dont have b- NOT sufficient
st2)q=b, dont have q- NOT sufficient
st1 and st2 togther
n=q=b so n=120/3=40
answer C
Total people= no. ppl of eating salads + no. ppl of eating no. of sandwiches + no. ppl of eating neither + no. ppl of eating both
given data and taking q,n,b as variables
300 = 180 +q + n +b, find "n"
120= q+n+b
n=120-q-b
St1) n= q, dont have b- NOT sufficient
st2)q=b, dont have q- NOT sufficient
st1 and st2 togther
n=q=b so n=120/3=40
answer C
