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

Irina on July 29, 2019

@mbarnett,

Let's look at the setup for this game.

We need to match grades ABCDE to courses Ec, G, H, I, P, R. Since we have 6 courses and only 5 grades to choose from, we will end up with at least one identical grade.

__ __ __ __ __
A B C D E

Let's look at the rules:

(1) G & P are consecutive
meaning it could be A &B, B&C, C&E etc.

we can diagram this rule as:

GP v. PG

(2) I &R are consecutive

but we have no information on the exact order so it could be:

IR v RI

(3) Ec grade is higher than H

E>H
__ __ __ __ __
A B C D E
~H ~E

(4) G grade is higher than P

G>P

combined with rule (1) we can determine that P must immediately follow G:

GP

__ __ __ __ __
A B C D E
~H ~E
~P ~G

Now, the question gives us additional rules to determine the order:

P grade is higher than Ec and Ec grade is higher than any language

P > Ec > I
> R

Combined with the rules above, we can determine the following:

GP > Ec > H
> IR
> RI

Let's diagram this:

/R /H
/I /R
G P Ec /H /I
__ __ __ __ __
A B C D E
~H ~E
~P ~G


We can determine the grades for G, P, and Ec but for the rest of the subjects we only know that H is lower than Ec, but we have no rule whether H & Ec are consecutive, so H could be D or E. We also know that Ec is higher than either I or R are that I &R are consecutive but we do not know whether I or R grade is higher, so either Ec -C, R -D, I-E or Ec-C, I-D, R-E could be the correct order.

What information do we need to determine all of the grades?

Let's look at (D) - R & H are identical.

This fact alone would still result in two possible combinations of courses & grades.

Option 1:
H
G P Ec R I
__ __ __ __ __
A B C D E

Option 2:

H
G P Ec I R
__ __ __ __ __
A B C D E

Since H &R could either be E or D, we cannot determine the complete order of the grades.

The correct answer choice (E) tells us that H is higher than R. This fact allows us to conclude that H & I are D and R is E.

H
G P Ec I R
__ __ __ __ __
A B C D E

Does this make sense?

Let me know if you have any other questions.

dtoukhlandjian@yahoo.com on June 12, 2023

Quick q:
doesn't "E" always come directly before "H". And "H" always come after "E" according to the rules. Because rule 3 and 4 are identical. In rule 4 "P" always comes after "G".

Emil-Kunkin on June 14, 2023

Hi, we know that P and G are consecutive from the first rule, not the fourth. The third rules does not tell us that E and H are consecutive, so they do not have to be.