Which one of the following could be the order, from first to last, in which the trucks arrive?

Victoria on November 2, 2020

Hi @ddamico212,

Happy to help!

We know that seven trucks arrive at a warehouse: S, T, U, W, X, Y, and Z.

No two trucks arrive at the same time. No truck arrives more than once, and the seven trucks are the only arrivals that day.

We also know that each truck is either R or G, but not both.

Therefore, we are dealing with a multi-linear game. We have seven trucks arriving in a sequence and each of these trucks needs to be assigned a colour.

_ _ _ _ _ _ _
_ _ _ _ _ _ _
1 2 3 4 5 6 7

Now let's go through the conditions.

Rule 1 - no two consecutive arrivals are R

This means that any truck arriving before or after an R truck must be G. However, it's also important to keep in mind that two or more G trucks could arrive consecutively.

Rule 2 - Y arrives at some time before both T and W

> T
Y
> W

This means that Y cannot arrive 6th or 7th.

Rule 3 - exactly two of the trucks that arrive before Y are R

This tells us that Y cannot arrive 1st or 2nd because at least two trucks must arrive before Y.

This also tells us that Y cannot arrive 3rd because this would mean that trucks 1 and 2 are both R, violating Rule 1.

Therefore, Y must arrive 4th or 5th.

Rule 4 - S is the 6th arrival

Rule 5 - Z arrives at some time before U

Z > U

So, what do we know so far?

_ _ _ _ _ _ _
_ _ _ _ _ S _
1 2 3 4 5 6 7

Since S must arrive 6th, T and W must arrive 5th and 7th. Therefore, Y can only arrive 4th.

Why?
Y cannot arrive 1st, 2nd, or 3rd without violating Rule 3.
Y cannot arrive 5th or 7th because it must arrive before both T and W.
Rule 4 tells us that S must arrive 6th. Therefore, T and W must arrive 5th and 7th.

This also means that we know the colours of trucks 1-4. We know that exactly two trucks which arrive before Y must be R and Rule 1 tells us that no two consecutive arrivals are R. Therefore, trucks 1 and 3 must be R and truck 2 must be G. This means that Y is also G because the 4th truck cannot be R as the 3rd truck is R.

R G R G _ _ _
_ _ _ Y T/W S W/T
1 2 3 4 5 6 7

We are looking for the answer choice which outlines one possible order in which the trucks could arrive. This should be pretty easy now that we have most of our variables mapped out above!

We can start by eliminating any answer choice where Y does not arrive 4th based on our deduction above.

Therefore, we can eliminate answer choices (B), (C), and (E) as Y arrives 2nd, 5th, and 3rd in these answer choices, respectively.

This means we have narrowed it down to answer choices (A) and (D).

We can also eliminate answer choice (D) based on our diagram above. We know from Rule 2 that Y must arrive before both T and W. In answer choice (D), T arrives before Y; therefore, this answer choice cannot be true.

Therefore, our correct answer choice should be (A), but let's double check. For the sake of ease, let's assume the RGRG pattern continues.

R G R G R G R
X Z U Y W S T
1 2 3 4 5 6 7

Notice that this meets all of our rules:

1) No two consecutive arrivals are R because the arrivals alternate between R and G.
2) Y arrives 4th i.e. before both W and T which arrive 5th and 7th, respectively.
3) Exactly two of the trucks that arrive before Y are R (1 and 3).
4) S is the 6th arrival.
5( Z arrives 2nd i.e. before U which arrives 3rd.

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