Q16

[aileenann]

A student asked:

Hi,

For question 16 why is the answer D? Couldn't there be two topazes? With a setup of FGJKXY?

Here's the explanation (note I'll be working off the diagram Noah posted earlier on this same thread):

If exactly 2 rubies are selected, that means that means that at least 4 of the jewels are accounted for - 2 rubies and then at least 2 topazes.

But do we know a little more? Yes, actually. Since exactly 2 rubies are selected, then we know it is not the case that exactly 1 ruby is selected. Since there is not exactly 1 ruby selected, using the contrapositive of constraint 2 on our original list, we know there are not exactly 2 sapphires selected. Since we can either have 1 or 2 sapphires, and 2 has been eliminated, we must have exactly 1 sapphire.

I hope this helps. Let me know if you have follow up questions or comments

[QIAOH648]

Hey,

The question said 2 rubies were selected. Answer E. Hypothetically speaking, if 2 topazes were selected, then, two sapphires must be selected. It violated the 2nd rule: 2S--->1R. There must be 1 sapphires selected here because there cannot be 2-2-2 or 2-0-4 structures in this game. Answers of A, B, C could be true.

So, D must be true.

Hope it works.

Can anyone explain Q17???? Thank you ~~~~

[Laura Damone]

Q17 has been answered in the forum for that question

[JenniferK632]

Do you disprove the other answer choices or, if you have numerical distributions already written out, do you consult those and move on? Thanks!

A student asked:

Hi,

For question 16 why is the answer D? Couldn't there be two topazes? With a setup of FGJKXY?

Here's the explanation (note I'll be working off the diagram Noah posted earlier on this same thread):

If exactly 2 rubies are selected, that means that means that at least 4 of the jewels are accounted for - 2 rubies and then at least 2 topazes.

But do we know a little more? Yes, actually. Since exactly 2 rubies are selected, then we know it is not the case that exactly 1 ruby is selected. Since there is not exactly 1 ruby selected, using the contrapositive of constraint 2 on our original list, we know there are not exactly 2 sapphires selected. Since we can either have 1 or 2 sapphires, and 2 has been eliminated, we must have exactly 1 sapphire.

I hope this helps. Let me know if you have follow up questions or comments

[Laura Damone]

Please forgive the delayed response here. We had a technical issue that caused this post to get buried!

No need to disprove answers in LG if you've found one that you can prove correct! That's true of numerical distributions, and any other inference you can make.

Hope this helps!