M40-114

Question

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.

Bunuel · Answer

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

RiyaGangar · Answer

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

Bunuel · Answer

You are wrong.

For (1):

Example 1: Salads = Neither = 80, Both = 40.
Example 2: Salads = Neither = 100, Both = 80.

Two possible values for Neither, so (1) alone is not sufficient.

Please study the OE.

anu12345678765 · Answer

180 employees ate sandwiches

How to know when it means they are eating only sandwiches? 
in general there is nothing specific so i took sandwiched and both together as equal to 180

Bunuel · Answer

“180 employees ate sandwiches” includes everyone who ate a sandwich, whether or not they also ate salads. If it meant only sandwiches, the problem would explicitly say “only sandwiches.”

iamyogi25 · Answer

Hi Bunuel,

Your solution is flawless as usual. I have done lots of similar problems using 2*2 matrix methodology as it is better for me to visualize. But the trouble of these problems with matrix methods especially in DS is the time constraint and tendency of mixing of 2 statements in the single matrix leading to errors. Just want to know your advice on which method would be most efficient in DS? Thank you.

M40-114

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