Which one of the following is a possible assignment of riders to bicycles, with the riders for each bicycle listed in...

Victoria on November 4, 2020

Hi @dtrer,

Happy to help!

We know that a cycling magazine is running a two-day study.

Four riders are participating in the study: R, S, T, and Y.

Each rider will test one bicycle on each day. Each rider tests a different bike on the second day than they test on the first day.

There are four bicycles: F, G, H, and K.

All four bicycles are tested each day.

You could set this up with either the bikes or the riders running vertically. I'm going to set it up using the bikes because that's how the answer choices are set up, but it would work just as well the other way if that makes more sense to you.
1 2
F: _ _
G: _ _
H: _ _
J: _ _

Now let's go through our conditions.

Rule 1A - R cannot test F

This means that R must test: (1) GH; (2) GJ; or (3) HJ. Note that the order can be flipped for each of these options.

Rule 1B - Y cannot test J

This means that Y must test: (1) FH; (2) FG; or (3) GH. As above, the order can be flipped for each of these options.

Rule 2 - T must be one of the testers for H

This means that either R or Y must test their respective second options as outlined above.

Rule 3 - the bike that Y tests on the first day must be tested by S on the second day

This means that Y cannot test H on the first day because T must also test H.

This also means that we cannot reverse options (1) or (3) outlined above under Rule 1B.

Therefore, Y must test either F or G on the first day. Note, however, that it is entirely possible that Y tests H on the second day if R does not test H.

Now that we've made a few deductions based on the rules, let's address the question stem. We are looking for the answer choice which outlines a possible assignment of riders to bikes.

We can immediately eliminate answer choices (A) and (D) because Rule 1 tells us that R cannot test F and Y cannot test J.

We can also eliminate answer choice (B) because Rule 2 tells us that T must be one of the testers for H. Here, Y and S test H.

Finally, we can eliminate answer choice (E) because Y tests F on the first day and T tests F on the second day. Rule 3 tells us that the bike that Y tests on the first day must be tested by S on the second day. This means that S should test F on the second day, but that is not the case here.

This means that answer choice (C) should be the correct answer, but let's double check!

F: Y S
G: S R
H: T Y
J: R T

Notice that this meets all of our conditions:

1) R does not test F
2) Y does not test J
3) T tests H on the first day
4) Y tests F on the first day. S tests F on the second day.

Hope this helps! Please let us know if you have any further questions.

dtrer on November 5, 2020

Thanks so much for the help!
Also, I was wondering if you had any tips for question stems that are very general, such as "which of the following could be true", "which of the following cannot be true", or "which of the following must be true". This game contained a few of those questions and I struggle with how to approach those questions.