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29 Apr 2025, 06:50
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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.
(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.
29 Apr 2025, 06:50
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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
25 Oct 2025, 23:07
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I don’t quite agree with the solution. If we consider no of employees having salad and neither as x,
Salad and Sandwich = 120
Salad not sandwich = 120 -x
Salad = x
Not Salad but Sandwich =60
No salad no sandwich = x
No salad = 300 -x
Total Sandwich = 180
Total no sandwich= 120
Total 300
Can be solved by this matrix to get x = 120
Salad and Sandwich = 120
Salad not sandwich = 120 -x
Salad = x
Not Salad but Sandwich =60
No salad no sandwich = x
No salad = 300 -x
Total Sandwich = 180
Total no sandwich= 120
Total 300
Can be solved by this matrix to get x = 120
