This question presents the following problem: "Of the 400 members at a health club, 260 use the weight room and 300 use the pool. If at least 60 of the members do not use either the weight room or the pool, then the number of members using both the weight room and the pool must be between:"

(A) 40 to 100
(B) 80 to 140
(C) 160 to 260
(D) 220 to 260
(E) 220 to 300

The correct answer is D. I did not understand the solution that used the process of elimination to arrive at D. Instead, I proceeded with drawing the Venn diagram and guessed the answer at the end.

So, here's what I did: On the left circle, I have weight room with 260. On the right circle, I have pool with 300. On the bottom, I have 60 for neither. On the top, I have 340 for weight room plus pool. Knowing that weight room plus pool cannot exceed 340, I subtracted 260 (weight room) from 340 and I got 80. After, I subtracted 300 (weight room) from 340 and I got 40. Then, I added the results together and I got 120. I subtracted 120 from 340 to get the lower limit of weight room and pool users, which is at 220. Knowing that there is a difference of 40 between two limits, I guessed answer D.

I'm unsure if I have the correct understanding of the Venn diagram. Since this question is testing my understanding of the Venn diagram, I would appreciate it if you can provide me with some feedbacks.