Answer to Question #102371 in Algebra for Tyreisha

Question

Brian is the coach of the High School basketball team in Scooterville. His starting five players (Jason, Mike, Jim, Dave, and Frank) all vary in their speed, height, and shooting ability. Use the following information to answer the question.

WHICH PLAYER IS THE TALLEST?

-Mike and Jim are quicker and better shooter than Jason and Dave
-No person is the best at more than one category
-One person was the worst for all three categories
-Jason is the third tallest
-Frank is the best shooter
-Jim is the second-fastest
-Jim is a better shooter than Mike

Answer 1

Let's draw a table to arrange all players at their categories columns depending on their abilities.

And give a letters to provided statements:

A) Mike and Jim are quicker and better shooter than Jason and Dave

B) No person is the best at more than one category

C) One person was the worst for all three categories

D) Jason is the third tallest

E) Frank is the best shooter

F) Jim is the second-fastest

J) Jim is a better shooter than Mike

Now we have to check each statement about players and find univocal ones.

That's about:

Jason is the third tallest (D)

Frank is the best shooter (E)

Jim is the second-fastest (F)

Now, assuming that 'No person is the best at more than one category' (B) we can expect that the tallest person should be one of these players: Mike / Jim / Dave. (Assumption 1)

Frank is already best at shooting (E), and Jason is already known as third tallest (D).

Either we can do for a fastest player: Frank is already best at shooting(E), and Jim is already known as second fastest (F). Expecting: Jason / Mike / Dave. (Assumption 2)

At this point, let's take a look at this statement: 'Mike and Jim are quicker and better shooter than Jason and Dave' (A)

As we already know, Frank is the best shooter (E), then we have only 4 places 'after' him, and taking into account that Mike and Jim are both better then Jason and Dave at shooting (A),

we can assume that Jason and Dave could be the 4th or 5th at shooting, while Mike and Jim could be at second and third places (Assumption 3).

Having in mind that 'One person was the worst for all three categories' (C) we can say that Jason is not that person, because of statement D, and taking into account our Assumtion 3, we can declare that Dave is that player that is worst at all categories. (Assumtion 4)

Now we can correct our Assumtion 1: Dave couldn't be the tallest, it should be one of these players: Mike / Jim (Assumtion 5)

And either do with Assumtion 2: Dave couldn't be the fastest, it should be one of these players: Jason / Mike (Assumtion 6)

Let's get back to statement A: Mike is quicker than Jason, so the Jason couldn't be the fastest. Taking into account Assumption 6, we can declare that Mike is the fastest player (Assumption 7)

And the last action: we know that the tallest player should be a Mike or Jim (Assumtion 5), we also know that Mike is the fastest (Assumtion 7), and using the statement B we can declare that Mike can't be the tallest, so it should be Jim.

So the answer is "Jim is the tallest player"