The test

Logic Level 2

There are three people, named Bob, Brad, and Kyle. They had just got their grades from a test. Bob shows his score to Brad and Kyle, but they don't show their scores to anyone. Nosy Nellie came along and wanted to know how the 3 of them did.

Brad truthfully says," I didn't get the highest score."

Kyle truthfully says,"I didn't get the lowest score."

Put their scores in order, from lowest to highest.

Brad, Bob, Kyle Bob, Kyle, Brad Kyle, Bob, Brad Kyle, Brad, Bob

2 solutions

Viki Zeta
Nov 10, 2016

Brad knows Bob's score and his own score, but not Kyle's score. Similarly, Kyle knows Bob's score and his own score, but not Brad's score.

Let Bob's score be $x$ , Kyle's score be $y$ , and Brad's score be $z$ .

The only way Brad can know that he I didn't get the highest score is if Bob got higher than Brad. $\implies z < x$

Similarly, the only way Kyle can know that he didn't get the lowest score is if Bob got lower than Brad. $\implies x < y$

From this, we infer $\implies z < x < y$ . Brad scored the lowest, Bob scored in between, Kyle scored the highest.

Then why is the answer Kyle Brad Bob? That goes directly against what you're saying, which I agree with, and what the problem says. The information in the problem says Kyle didn't get the lowest score, and yet he has the lowest score according to the answer.

Emily Namm - 4 years, 7 months ago

The answer is Brad, Bob, Kyle look carefully.

Viki Zeta - 4 years, 7 months ago

The solution could be improved by being more explicit in the logical reasoning. E.g. When Brad says that he didn't get the highest score, there are 2 possibilities of 1. Bob scored higher than Brad, 2. Kyle scored higher than Brad. We should explain why the second possibility should be eliminated.

Calvin Lin Staff - 4 years, 7 months ago

Reading the problem I understood that Bob showed his result to Brad and Kyle TOGETHER so they know each other's response as in the drawing where there are together. In that case there is no solution and either Brad or Kyle is lying. It should be said that that Bob showed his result to Brad and Kyle separately.

Yves Hausermann - 4 years, 7 months ago

Also maybe next time add additional options to choose from. 3 of the 4 can be eliminated directly, because the first two have Kyle scoring lowest and the third one has Brad scoring the highest.

Kai Ott - 4 years, 7 months ago

Fredrick Lue
Nov 9, 2016

If Kyle did better than Bob, he wouldn't know that he didn't get the highest. Same goes with Brad.

The test

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