M40-117

Question

At a manufacturing plant, each department has at least one worker. Are there more workers in Department A than in Department B?

(1) 75% of the workers in Department A also work in Department B.
 
(2) 40% of the workers in Department B do  not  work in Department A.

Bunuel · Answer

Official Solution:

At a manufacturing plant, each department has at least one worker. Are there more workers in Department A than in Department B? 
 
(1) 75% of the workers in Department A also work in Department B.
 
This implies that {Both} = 0.75A, from which we cannot answer the question. Not sufficient.
 
(2) 40% of the workers in Department B do  not  work in Department A.
 
This implies that the remaining 60% of the workers in Department B  do  work in Department A. Thus, {Both} = 0.60B. From this however, we cannot answer the question. Not sufficient.
 
(1)+(2) From above we get that 0.75A = 0.6B, which gives 5A = 4B and finally A/B = 4/5, which means that Department B has more workers than Department A. Sufficient.
 
Answer: C

705in11112025 · Answer

I used number testing here, assumed 40 worker for Dept A.

komatsu · Answer

I like the solution - it’s helpful.

YellowChalk · Answer

i do not agree with the solution here, there is nothing in the question that says Manufacturing plant only have 2 departments, so statement 2 : "40% of the workers in Department B do not work in Department A." DOES NOT necessarily mean 60% of workers of department B works in department A. There may be department C or D or E where they might be working.

Bunuel · Answer

Statement (2) is not assuming that the plant has only two departments. Among workers in Department B, each worker either works in Department A or does not work in Department A. So if 40% of B do not work in A, the remaining 60% of B must work in A. Those workers may also work in C, D, etc., but that is irrelevant.

M40-117

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