[DS strategy] When both statements give the same information

[SK191]

Hello,

I was just watching Thursday with Ron December 11, 2014 and he mentions an interesting point at the 1:06:15 mark.

Both the statements of the DS question were giving the same information.

So Ron remarked that since both the statements are giving the same information, then the answer can't be C or E.

Why is that?

Thanks! I'm sorry if im digging into an old video too much. haha. But i found this point very interesting.

Best wishes.

[tim]

I have looked at the video. First, this is not a problem where the statements are the same; rather, it is a problem where one statement implies the other. This generates a somewhat different strategy.



Take this pair of statements for example, where statement 2 implies statement 1:

1) x > 5
2) x > 7

First, C is out. Combining the facts x>5 and x>7 yields x>7, so we do not get any additional information by combining the two (in other words, in this case it is impossible for both statements together to be sufficient but neither by itself, because if the statements together were sufficient, 2 would be sufficient on its own).

Second, A is out. Because statement 2 implies statement 1, if statement 1 is sufficient then statement 2 must be sufficient as well (if knowing that x>5 will definitively answer the question, then knowing that x>7 will also answer the question, because knowing that x>7 means we also know that x>5).



Just for fun, let me demonstrate questions that will allow the answer to be B, D, or E (I'll let you verify the solution on your own):

Is x > 6? (answer is B)

Is x > 4? (answer is D)

Is x > 8? (answer is E)

I suspect Ron simply misspoke when indicating that C and E were out; sorry for the confusion.



BTW if the statements do in fact state exactly the same thing, then the answer must be D or E (A, B, and C are all out), because there is no way one statement can work without the other working (eliminating A and B), and there is no point combining statements that are identical (eliminating C).

[SK191]

Thank you very much for your prompt response. My question has been answered. You going the extra mile and explaining with an example is greatly appreciated.

Regards

[RonPurewal]

hm, weird. i make lots of mistakes, so it's certainly possible that i made one there.

in any case, the whole truth is:

IF STATEMENTS 1 & 2 ARE EXACTLY THE SAME...
...A, B, C are impossible
...effectively there's only one 'statement'
...if 'the statement' is sufficient, answer is D
...if not, answer is E

IF STATEMENT 1 IS A SUB-SET OF STATEMENT 2...
(e.g., statement 1 says x > 20, statement 2 says x > 10)
...B, C are impossible
...if statement 1 is NOT sufficient then answer is automatically E (since the same cases will work for statement 2)
...if statement 2 is sufficient then answer is automatically D (statement 1 removes cases from statement 2; if there's only one outcome before that removal, there will certainly still be only one afterward!)

IF STATEMENT 2 IS A SUB-SET OF STATEMENT 1...
...A, C are impossible
...basically just the reverse of the above

[RonPurewal]

...so, yeah, i possibly made a mistake.

THE MOST IMPORTANT THING TO NOTE HERE, though, is that this is basically just all 'nerd fun' and almost certainly will NOT prove useful in actually solving the problems.

basically, it's just too complicated.

e.g., consider the middle group of statements (about a situation such as '#1 says x > 20, #2 says x > 10').
which would be easier...
...thinking about 'hmm, #1 is a sub-set of #2, therefore blah blah blah'?
or...
...just treating the statements like any other statements?

i would bet lots and lots of money that the former is ALWAYS substantially more difficult, and that the latter is ALWAYS substantially less difficult.

so, just nerd fun.
(:

[SK191]

haha! You're right! Its probably more time consuming and more prone to error in stress situation.

I watch Thursday's with Ron religiously and has helped me greatly. So this particular point piqued my interest and thought i'd ask you guys. Thanks for the response.

And i understand the slip of tongue with the letters. I'm still amazed how Thursdays with Ron and access to this forum is free. Invaluable!

.... it is free right?

[tim]

Yes it is free (you haven't paid for any of them, have you?). Glad you find the classes helpful.

And I echo Ron's observation that it's all just nerd fun. Under the time pressure of the test, you have much more important things to worry about than this.

[RonPurewal]

haha! You're right! Its probably more time consuming and more prone to error in stress situation.

...or even in completely stress-free situations, such as when ron is hosting 'thursdays'.
(:

(i watched the recording and, yes, you're correct—i said something that was totally wrong. who knows, maybe i meant to say something else.
in any case, nice catch.)