Can you explain this PSAT problem?

[Nan in Mass]

If x=4, then y>3.

If the statement above is true, which of the following statements must also be true?

A) If x>3, then y=4.
B) If x not equal to 4, then y not equal to 3.
C) If y>3, then x=4.
D) If y<3, then x not equal to 4.
E) If y<3, then x=4.

I had no trouble with the rest of the PSAT math, but neither my son nor I understand this question.
-Nan

[creekland]

Yes, I can explain it, but if it's one from this year's test and anyone from collegeboard finds out it was put online it will invalidate the tests from the school that student was in. They are not allowed to discuss questions or post questions from this year's test...

If it's from a practice test, let me know and I'll explain it.

[creekland]

Ok, I just asked my son and he told me the problem came from the practice test booklet - phew! No problem explaining it then...

The answer is D because in truth tables and if/then statements... when given a true statement the only other true statement is if both are negative and switched in order. For example...

If A, then B also means if NOT B, then NOT A.

In this specific example, if x = 4 then y > 3 is given as true. Therefore, the 'nots' for each are if y < 3, then x can't equal 4. If it did, the first statement would be false.

Choice C is the 'trick' answer, but truth tables simply don't work that way...

Let me give an easier example.

If I live in Gettysburg, then I live in Pennsylvania.

The alternative truth answer is if I do NOT live in Pennsylvania, then I don't live in Gettysburg.

The trick (wrong) answer would be if I live in Pennsylvania, then I live in Gettysburg.

It's easy to see why it doesn't work when given 'facts' like these, but the same is true for variables of all sort.

Is that more clear now? I'm typing off the top of my head... while concentrating on other things... so...

Edited to add that of course I'm talking about Gettysburg, PA, not Gettysburg from any other state... :)

[Nan in Mass]

Why isn't y < or = 3? Why is it y < 3? What happened to the case when y = 3? That is one thing that confuses me. But even more than that, they didn't ever say that there weren't other Gettysburgs in other states, so we couldn't figure it out. I take it that they are refering to some sort of system of logic, with their x's and y's and if/then's that we should have recognized, one in which there is an underlying assumption that they didn't bother to specify, that being that there aren't Gettysburgs in other states? Something having to do with ranges and domains or something? Obviously, I've forgotten a lot LOL.
-Nan

[Julie in MN]

Why isn't y < or = 3? Why is it y < 3? What happened to the case when y = 3?

It could be equal to 3 or less than/equal to 3, and it would still work. But since that wasn't a choice, the less than 3 one also works.

But even more than that, they didn't ever say that there weren't other Gettysburgs in other states, so we couldn't figure it out.

Gettysburg in her example is the exact Gettysburg that is being identified, and none other. We know that because she's using it as an example of "3" -- 3 is 3. You can't have various 3's in other states that mean something different!

[creekland]

I agree with Julie. It could easily have been y = 3 and still worked as well - or y = 2 or y = anything not greater than 3.

By the first statement being 'given' as true, even if I didn't go back to edit my 'Gettysburg' example, it still eliminated all the other Gettysburgs out there. They told us the first statement is true... that's the assumption we are told to go with.

[Nan in Mass]

Ok. I understand the y=3 problem. That looks obvious to me now. I think the bit I missed was "first statement given as true" bit LOL. I know it seems obvious, but that isn't that obvious if you are a computer programmer. If/then statements aren't statements of truth, they are statements of possible truths and future actions. That first statement is much more universal and immutable than I was assuming. It was stupid of me not to see that, but I had just spent the morning trying to gobble down a new programming language after twenty years of hardly touching the stuff LOL. If the question had dealt with Gettysburg in the first place, I would have understood it. It is obvious stated like that. It was the x's and y's combined with if/then statements that threw me off. Thank you both for explaining it. It isn't easy explaining the obvious GRIN.
-Nan

[creekland]

... I think the bit I missed was "first statement given as true" bit LOL. I know it seems obvious, but that isn't that obvious if you are a computer programmer. If/then statements aren't statements of truth, they are statements of possible truths and future actions. That first statement is much more universal and immutable than I was assuming.

That's true. Ah, the good ole days of computer programming. I don't actually do any of it anymore - other than the occasional spreadsheet, but, of course, that's totally different.

If the question had dealt with Gettysburg in the first place, I would have understood it. It is obvious stated like that. It was the x's and y's combined with if/then statements that threw me off...

And this is why I use such an example when teaching the concept to students at school. It helps that we live near Gettysburg. :) In general though, it's far easier to understand it with the x's and y's when one understands the overall first IMO.

If it makes you feel any better... that question is the only one my son missed on the practice test when he took it... :) He fell for the trick answer. In a huge way, I'm glad he missed it on the practice test so he is now well-prepared for these types on all future tests. Once he misses something he never gets it wrong thereafter... not conceptually anyway - there's always the occasional 'idiot error.'

[Nan in Mass]

Thank you.

I know what you mean. I worry about all the answers my son guessed on on the practice test. We won't go over them and he won't learn how to do them. Well, I don't really worry because it is just the PSAT and he is in 9th grade (at least on paper), but you know what I mean.

It has been so long since I programmed that I don't know any object-oriented programming languages. This new one (ChucK) is fun for me because it is. My only problem is that I need to know it in a hurry. Like last weekend GRIN.

-Nan