The Hale Imaging Core rents time on its electron microscope

What we see: a Multi-Source Reasoning set with 3 tabs: the rules, the list of requests, and the rates. Every question needs the rules applied to the list in the right order, so the first job is to run the review once and write down what gets approved.

Step 1. Put the requests in review order.
What we see: the rules review by funding level first. The submission date only decides the order inside one level.
What it means: external first, 2 (March 11) then 5 (March 12); internal grants next, 1 (March 9), 6 (March 10), 4 (March 12), 8 (March 13); unfunded last, 3 (March 10) then 7 (March 11).
What we do and why: go down that list once, keeping track of the approved times and each group's approved hours.

Step 2. Run the review.
What we see: three tests for each request: the time is free, the group stays at 8 hours or less, and a group with no certified operator stays at 4 hours or less.
What it means:
Request 2, Brandt, Monday 10 a.m. to 1 p.m., 3 hours: nothing approved yet, so approved. Brandt has no certified operator, so its limit is 4 hours.
Request 5, Brandt, Wednesday, 2 hours: Brandt would reach 5 hours, over its 4, so refused.
Request 1, Okafor, Monday 8 a.m. to 12 p.m.: overlaps request 2 from 10 to 12, so refused, even though it was submitted first.
Request 6, Ferraz, Wednesday 8 to 11 a.m., 3 hours: the time is free because request 5 was refused, and 3 hours is within Ferraz's 4, so approved.
Request 4, Okafor, Tuesday, 3 hours: approved. Okafor has 3 hours.
Request 8, Okafor, Friday, 3 hours: Okafor reaches 6 hours, within 8, so approved.
Request 3, Liu, Tuesday 1 to 6 p.m.: overlaps request 4, so refused.
Request 7, Liu, Thursday, 4 hours: approved.
What we do and why: approved requests are 2, 4, 6, 7 and 8. All three questions read from this list.

Step 3. Question 1.
What we see: requests 1, 5 and 8.
What it means: request 1 lost its time to request 2, which has higher priority; request 5 breaks Brandt's 4-hour limit; request 8 leaves Okafor at 6 hours.
The trap here: approving request 1 because it was submitted first. The date only matters inside one funding level.

Step 4. Question 2: the bill.
What we see: only approved hours are billed, and an hour that begins before 9 a.m. costs half.
What it means: Brandt \(3 \times 240 = 720\). Ferraz's first hour starts at 8 a.m., so \(55 + 2 \times 110 = 275\). Okafor \(6 \times 110 = 660\). Liu's first hour starts at 8 a.m., so \(35 + 3 \times 70 = 245\).
What we do and why: \(720 + 275 + 660 + 245 = 1{,}900\) dollars.
Each wrong choice comes from one slip: 1,990 forgets the half-price hours; 1,685 bills a whole session at half price when it starts before 9; 2,285 also bills refused request 1; 2,380 approves request 5 by missing the 4-hour limit.

Step 5. Question 3: run the review again without request 2.
What we see: one request leaves, so every later decision can change.
What it means: request 5, Brandt, now has 0 hours before it, so it is approved for Wednesday 9 to 11 a.m. Request 1 now finds Monday free and is approved, giving Okafor 4 hours. Request 6, Ferraz, Wednesday 8 to 11 a.m., now overlaps request 5, so it is refused. Request 4 brings Okafor to 7 hours. Request 8 would bring Okafor to 10 hours, over 8, so it is refused.
What we do and why: request 5 would be approved; requests 6 and 8 would not.

The trap: in Question 3, thinking that removing a request can only help the others. Here it lets requests 5 and 1 in, and they push out requests 6 and 8.
Takeaway: With a rules tab and a list, run the whole process once, in the stated order, with a running tally. A "Suppose" question means running it again from the start, because one change can ripple through every later step.

Answer: 1. No, No, Yes. 2. 1,900 dollars. 3. Would be approved, Would not be approved, Would not be approved