If John receives a higher grade in physics than in economics and receives a higher grade in economics than in either ...

AneeshU August 3, 2020

How was it concluded that John got an 'A' in G?

Hi. In the explanation for this solution, I'm not able to understand how it was concluded that G is an 'A'. Although I see that the method of process of elimination is used, there is no condition which states that there must be a subject in which John scored an A. So, just as it is possible that John did not fail any subject, it must also be possible that John did not get an A in any subject. My understanding is that if we don't know for certain that John got an A in any of the subjects then we can't use the process of elimination to find a subject which would fit in that category. What am I missing??

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shunhe August 3, 2020

Hi @AneeshU,

Thanks for the question! So first, let’s talk about what the prompt has us assume. John gets a higher grade in P than E. But remember that John’s grades in P and G are consecutive, so G is also going to be higher than E. And G is actually a higher grade than E, so now we know that

GP — E

Now John also receives a higher grade in E than in either language, which are I and R. So E is in front of both of them, and they’re also consecutive. So now we know something like

GP — E — R/I I/R

And notice here that we already have all five grades taken up. Geology is ahead of P, E, R, and I, each of which have to have a different grade. And G also has to be in a separate one. So G has to be an A grade. In fact, we can even say the following:

A: G
B: P
C: E
D: R/I
E: I/R

And that’s how we know that John has to get an ‘A’ in G. If John got a B, for example, then there wouldn’t be room for the other grades.

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

heatherdianne5 January 9, 2021

How do we distinguish between R and I? It said which would determine all of the grades. But i don't see how we can determine what I and R are. It just says that are consecutive. How do I know which is D and which is E?