How do I attempt this problem without throwing my laptop out the window?

[Irving4Prez]

Tried to get my head around this problem by drawing venn diagrams and it took me 2-3 minutes to trial and error. The suggested solution was difficult to comprehend and I just keep repeating this phrase without getting anywhere, "if one of the statements is true, then the other is also true... if one of the statements is false, then the other is also false". How would you attempt a question like this?

[datfatcat]

Hi,
Use trial and error + venn diagram. Say statement I is true, what would happen in the venn diagram is that the circle P (Ploys) would be within circle Q (Quoys). Now see the rest of the statements and see if they are correct or false. Statement 2, 3, 4 are wrong because they are not possible under statement 1. Hence, if statement 1 is correct, other statements are wrong (so you are left with answer B). Use the same logic and see why answer B is correct yourself!

[Irving4Prez]

Ah, thank you. When they say both statements are false, does that mean "some ploys are quoys" instead of, "some plays are not quoys" and "some ploys are quoys" instead of, "some, but not all, ploys are quoys"?

[alchemy]

Umm, I don't intend on doing the UMAT or anything but, can "some Ploys" mean "all ploys" as stated by the second statement? Is the third statement sufficient to verify this, as it states that "some but not all"?

Also, for your question, I guess your answer is incorrect because it asks for what can be both true and both false. Option C suggests that both statements are true but not both statements are false.

[Irving4Prez]

Umm, I don't intend on doing the UMAT or anything but, can "some Ploys" mean "all ploys" as stated by the second statement? Is the third statement sufficient to verify this, as it states that "some but not all"?

Also, for your question, I guess your answer is incorrect because it asks for what can be both true and both false. Option C suggests that both statements are true but not both statements are false.

All ploys would suggest 'some ploys' not the other way around and I guessed C as it was taking too much time

[datfatcat]

OK I made two venn diagrams for you (poor photoshop skill hehe). Say statement 1 is correct. The diagram would look like the one on the left. If we look at statement two, it says some ploys are not quoys. This cannot be true because every ploys is quoys (the whole ploys circle is within quoys and not a tiny bit outside quoys). If statement two is true, the venn diagram would look like the one on the right. Hence statement 2 cannot be right if statement 1 is true. Same logic applies to statement 3 and 4 and with our venn diagram on the left, we can say they are all wrong. So if statement 1 is true, no other statement can be true (hence all the options with statement 1 are wrong and left us with option B) So how can option B be correct? We can give it a try. Say statement II is correct (right venn diagram). For statement III, it is correct because part of the circle representing ploys is within quoys (but part of it is outside (hence "not all" are quoys)) So statement II and III are both correct at the SAME time. Now try and figure out if they are both wrong at the same time. If statement II is false, it means every ploys are quoys (hence statement 1 is true (left venn diagram)) and if you remember what I tried earlier, if statement 1 is true, all the rest are false. Hence statement II and III are false at the same time. Option B is the right answer.

[Irving4Prez]

Aha, your explanation made up for the poor photoshop skill. Thanks

[alchemy]

OK I made two venn diagrams for you (poor photoshop skill hehe). Say statement 1 is correct. The diagram would look like the one on the left. If we look at statement two, it says some ploys are not quoys. This cannot be true because every ploys is quoys (the whole ploys circle is within quoys and not a tiny bit outside quoys). If statement two is true, the venn diagram would look like the one on the right. Hence statement 2 cannot be right if statement 1 is true. Same logic applies to statement 3 and 4 and with our venn diagram on the left, we can say they are all wrong. So if statement 1 is true, no other statement can be true (hence all the options with statement 1 are wrong and left us with option B) So how can option B be correct? We can give it a try. Say statement II is correct (right venn diagram). For statement III, it is correct because part of the circle representing ploys is within quoys (but part of it is outside (hence "not all" are quoys)) So statement II and III are both correct at the SAME time. Now try and figure out if they are both wrong at the same time. If statement II is false, it means every ploys are quoys (hence statement 1 is true (left venn diagram)) and if you remember what I tried earlier, if statement 1 is true, all the rest are false. Hence statement II and III are false at the same time. Option B is the right answer.

Makes much more sense now. Who cares about photoshop skill, that diagram sets everything clear.