Which one of the following must be true?

hkolon on May 30, 2020

Explain D

Can someone please explain why D is wrong and how to get the correct answer? Thanks!

shunhe on May 30, 2020

Hi @hkolon,

Thanks for the question! So it’s going to be a bit hard for me to diagram this one out for you, but if you’ve diagrammed this correctly, you should be able to follow along with what I’m saying here. And it also makes sense just based on the rules, but having a diagram will help you visualize what I’m about to write.

So this is a must be true question, and so we have to ask ourselves when considering (D), it is always the case that no more than three valves are opened after H is opened? Is there a way to open four valves? Well, clearly, O, L, and G can go after H. We’re told that O is opened after H, and that L is after O. We’re also told that L is after G, but we’re not told anything about the relative positions of H and G, which means that G can go after H. And finally, we’re not told anything about the relative positions of I and H. We’re told that I goes after K, but I could go after K and also after H. But that means there are four possible valves that can go after H: G, O, L, and I. And that means that (D) isn’t necessarily true, because we could have (for example) the following order:

PKNHOGLI

What has to be true based on the diagram? Take a look at (E), which tells us that no more than four valves are opened before N is opened. How many people can go before N? Well, H has to follow N, which means that O and L also have to follow N (since they follow H). But all the rest could go before N, which would make four total: IKPG can go before N, but the others can’t, which means that no more than four valves are opened before N is opened. Again, this is because H has to follow N (based on the fourth rule), and O and L follow H (based on the second rule).

Hope this helps! Feel free to ask any other questions that you might have.