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by allfta » Sat Jun 12, 2010 9:10 pm
Thank you for all!

If # represents one of the operations +,-,and x, is k # (l+m) = (k # l) + (k # m) for all numbers k, l, and m?
1) k # 1 is not equal to 1 # k for some numbers k.
2) # represents subtraction.
Answer]D

In this question, both #s of 1) and 2) are minus. right?
So, the answer of the initial question is "NO". right?
I wonder that I can choose D because I can say "No" but not because I cann't say whether the answer is yes or no.
Consequently, is it still ok when the answer is "no" but rather "yes" to answer the DS quetion?

So, If
1) # represents +
2) # represents +
then the answer is still D

and, if

1)# represents x
2)# repreestns +
then the answer is E?
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Source: — Data Sufficiency |

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by Rahul@gurome » Sun Jun 13, 2010 1:41 am
The answer to this question is definitely "no". It is not necessary that the question should have the answer "yes", the thing is we should have a definite answer. (I hope that is what you want to ask?)

If the operator is "+", then k + (l+m) = (k + l) + (k + m) = 2k + (l + m), which implies k = 2k, but k is not equal to 2k for all values of k. So, # cannot represent "+". So, the answer is "no" here.

If the operator is "-", then k - (l+m) = (k - l) + (k - m) = 2k - (l + m), which implies k = 2k, but k is not equal to 2k for all values of k. So, # cannot represent "-". Again the answer is "no".

Lastly, if the operator is "*", then k * (l+m) = (k * l) + (k * m) = kl + km, which implies kl + km = kl + km, which definitely is true for all values of k. So, the answer here is "yes".
So, the question can be rephrased as "Does # represent the operator multiplication?" And then we go to each of the statements.

(1) k # 1 is not equal to 1 # k for some numbers k.
If # = "+", then k + 1 = 1 + k is always true. So the operator is not "+".
If # = "-", then k - 1 = 1 - k is only true when k = 1. So the operator may be "-".
If # = "*", then k * 1 = 1 * k is always true. So the operator is not "*".
Hence, # is the operator "-" from statement 1, and the answer to the main question is definitely "no". So, (1) is SUFFICIENT to answer the question.

(2) Since # is clearly "-" here so, again the answer to the main question is definitely "no". So, (2) is SUFFICIENT to answer the question.

The correct answer is (D).
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by allfta » Mon Jun 14, 2010 5:30 am
Thank you Rahul@gurome,

You point my point. lol. I wondered whether the answer is still "sufficient" even if it says "NO" to a quetion but not "Yes"
Your explanation is yes it is still sufficient. So, we can choose D. It is clear.

But, as I asked in original post, what is the answer if
1) is +
2) is +

or

1) is +
2) is * ?

I thought the first case is still D because the answers of both condition are "No" and they are still sufficient to answer.
And in the later case, I think the answer is E because the answer of 1) is "NO" and the 2) are both "Yes" and we, consequently, can not say whether it is Yes or No.

So, this logic is right?
Many of OG quetions don't handle this No type sufficency quetions so I think this is worth to think about.
your confirmation plz.
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by Rich@VeritasPrep » Mon Jun 14, 2010 7:55 am
Hey there,

Let's address your two hypotheticals:

If the following were true...

1) is +
2) is +

...then yes, the answer would still be D. The prompt boils down to "Does # represent multiplication?" And as you've pointed out, both of these Statements would give you a definite "No", which means you have sufficient info to answer the question.

Now let's look at the second hypothetical you mentioned:

1) is +
2) is *

Believe it or not, this is actually impossible on the GMAT. Why? Because on real GMAT questions, the two statements never contradict one another. You've given a situation in which we have a contradiction, because # ends up being two different things.

Remember, on a YES/NO question like this, a statement is insufficient if you can get both a yes and a no WITHIN THE SAME STATEMENT. And you only combine statements when you've already concluded that EACH STATEMENT GIVES YOU A YES AND A NO INDIVIDUALLY.

But you will never see a question in which one statement leads to a yes-only and the other leads to a no-only, because that would be a contradiction.

Now, if you were given this...

1) is * or +
2) is * or +

...then that would be legal, because there's no contradiction...just incomplete information. The answer here would in fact be E, because each statement gives you both a yes and no, and when you combine the two statements, you get no additional information, since they are identical.

Make sense?
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by Testluv » Mon Jun 14, 2010 11:23 pm
You point my point. lol. I wondered whether the answer is still "sufficient" even if it says "NO" to a quetion but not "Yes"
Your explanation is yes it is still sufficient. So, we can choose D. It is clear.
Correct. If you get a "DEFINITE no" or a "DEFINITE yes" the statement is sufficient. It should be noted, however, that on the actual GMAT a statement that is sufficient to answer a yes/no question leads to a DEFINITE yes rather than a DEFINITE no more than 95% of the time.

But knowing that Definite no is sufficient is very helpful for rephrasing questions. For example, a question like this "Is x a non-integer?" can be safely rephrased to "Is x an integer?"
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by allfta » Tue Jun 15, 2010 5:37 am
@ raz1024
Sure. You got a point. But, if this type - 1)+ 2)* type - of quetion is really presentd in real test, I'd rather to choose E but not D. Because even if they still give answers individually, but, the contradiction makes us the answer still don't know just as 1)+ or * 2)+ or * type do.

Because there is no imformation whether 1) and 2) are linked with "and" relationship or "or" relationship. :) Then, if this type is really presented, this presentation natually means that the relation is "or". (Because if it means "and" it doesn't totally make sense) Then, it can be solved with the same logic which 1)+ or * 2)+ or * type has.

Anyway, I fully agree that this type will not be definitly given. haha.
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