# If mannequin 2 wears the red jacket, then mannequin 1 must wear the

filozinni on June 30, 2020

Why is D wrong

I don't understand why D is wrong. I got down to B and D and guessed B, but I don't see how one is correct and the other is wrong. Could anybody please explain? Thank you!

Replies

shunhe on June 30, 2020

Hi @filozinni,

Thanks for the question! OK, so let’s work through this to figure out why (D) is wrong. Let’s say that mannequin 2 has a red jacket. OK, so now we know that mannequin 2 has a red jacket and a navy skirt. Well, there’s only three colors, navy, red, and yellow. And we know that the hat can’t be the same color as the jacket, so mannequin 2 can’t wear the red hat. But it also can’t wear the yellow hat since neither mannequin wears all 3 colors. So we know that mannequin 2 wears the navy hat.

Now what do we know about mannequin 1. Well, mannequin 1 is wearing a red tie. And now we know that mannequin 2 is wearing the red jacket, so mannequin 1 can’t wear the red jacket. So mannequin 1 has to wear either the yellow or the blue jacket. But either way, the color of mannequin 1’s hat has to be different from the jacket, and it can’t be the third color. So let’s say mannequin 1 wears the yellow jacket; then mannequin 1 has to wear the red hat, since mannequin 1 can’t wear all three colors (so can’t wear the navy hat), and the hat has to be a different color from the jacket (so can’t be the yellow hat). Same if mannequin 1 wears the blue jacket, then mannequin 1 has to wear the red hat, since mannequin 1 can’t wear all three colors (so can’t wear the yellow hat), and the hat has to be a different color from the jacket (so can’t be the navy hat). So no matter what, mannequin 1 has to wear the red hat. And that’s why (B) is the correct answer.

(D), on the other hand, isn’t necessarily true. Mannequin 1 could wear a skirt that matches its hat color or a skirt that matches its jacket color, so there’s two choices there, it can wear either the red skirt or the yellow skirt (if it wears the yellow jacket). So (D) doesn’t have to be true and is the wrong answer.

Hope this helps! Feel free to ask any other questions that you might have.

filozinni on July 2, 2020

Thank you so much for the explanation @Shunhe!

shunhe on July 2, 2020