Which one of the following could be an accurate inventory of the flowers in Ursula's arrangement?

Victoria on May 18, 2020

Hi @libbymunoz,

Happy to help!

What do we know?

There are five individuals: S, T, U, W, and Z

Each person makes an arrangement of exactly four individual flowers.

S: _ _ _ _
T: _ _ _ _
U: _ _ _ _
W: _ _ _ _
Z: _ _ _ _

Each person uses exactly three kinds of flowers. This means that there will be two of one kind of flower in each arrangement.

Now let's go through the conditions.

The first condition can be rewritten to say: only S uses 2 roses.

2R --> S

Not S --> Not 2R

S: _ _ R R

The remaining two flowers in this arrangement must be different.

(2) T uses exactly one H and one G. We know that S can be the only one to use two Rs. Therefore, T can have either two Gs or two Ls.

T: H G G R/L * (only L is possible here - see below for explanation)

T: H G L L

(3) U uses exactly one R and at least one H. Therefore, there are several options here.

U: R H H L

U: R H H G

U: R H G G *

U: R H L L *

(4) W uses two Gs. The remaining two flowers must be different. Therefore, there are also several options here.

W: G G R L

W: G G H L

W: G G R H *

(5) Z and no one else uses exactly one H and exactly one R. Similar to the first, condition, this can be rewritten to say that only Z uses exactly one H and exactly one R.

1H and 1R --> Z

Not Z --> Not 1H and 1R

Notice that this removes some of our earlier possible diagrams. I've put an asterisk next to these.

(6) Exactly one person uses two lilies. This doesn't immediately eliminate any options above, but may do so depending on the question stems that follow. The possible individuals who could have two Ls are Z or T based on the diagrams above.

OVERALL

Z: H R G/L G/L

U: R H H G/L

T: H G L G/L

W: G G L R/H

S: R R G/H/L G/H/L (remaining two must be different)

Let's use this set-up to attempt Q1. This question asks us which could be an accurate inventory of U's arrangement.

Let's go back to our possibilities for U:

R H H L

R H H G

Notice that the second option is reflected in answer choice (D) making this the correct answer.

Answer choice (A) is incorrect because there is no H.

Answer choices (B) and (E) are incorrect because only Z can have exactly 1H and 1R.

Answer choice (C) is incorrect because only S can have 2R.

This is definitely a longer set-up, but the extra effort pays off! We now have a list of all possibilities for each flower arrangement, making it much faster to go through the questions.

Hope this is helpful! Keep up the good work and please let us know if you have any further questions.

Rachel on June 22, 2020

This is really helpful, but I agree that a video explanation would be even more helpful-- the text explanation is kind of overwhelming.

Ben on June 27, 2020

Hi Rachel, thanks for the feedback.

We are currently working on getting more video explanations out for the games so hopefully there will be more at your disposal at some point soon, but in the meantime, for all those games that a video explanation isn't ready for now please do reach out and we will do our best to help through the message boards!

Best of luck with your studies!