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"Can" vs "yes/no"

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jnorton1547 Junior | Next Rank: 30 Posts Default Avatar
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"Can" vs "yes/no"

Post Wed Feb 06, 2013 12:02 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    I will post this topic in both threads since it deals with both question types.

    On one my first practice CATS, I came across the following data sufficiency question:

    "Can the positive integer "a" be written as the sum of two different prime numbers?"

    The solution I worked toward took the meaning of "can" to mean, "can it - even one time - be sum of two different prime numbers given whatever combination of the statements may lead to?" Low and behold, I answered incorrectly and the explanation provided that because neither statement was "always yes" or "always no", neither was sufficient.

    So I tucked the fact that "can" doesn't negate the "always" aspect of these questions in my memory bank and moved on.

    Fast forward to today. I just finished another set of practice problems and I came across this problem solving question:

    "The average of a series of consecutive integers is an even integer. Which of the following could be true?
    I. There is an even number of integers in the series.
    II. The smallest number in the series is odd.
    III. The product of the smallest and largest number in the series is odd."


    Now, I have flashes of memory going off to disregard the "could" (as a relative of "can"), and to answer the question on the basis of being absolute. However, I did take in that this was a problem solving question, and in this case, I rightfully disregarded this new rule - to disregard "can" ( so now I'm in a double negative situation where I'm disregarding rules to disregard)- and answered correctly.

    HOWEVER - it brings up this "do I disregard something, and what do I disregard" dilemma that I worry about unless I'm given some kind of rule or logic to apply in these cases.

    So here is what I'm currently setting out to operate with, and I would appreciate any feedback:

    In ALL data sufficiency questions, no matter what the test makers may be trying to do by including a word like "can" in the question stem, I should abide by the "always yes" or "always no" philosophy.

    Then, with respect to problem solving questions, I should take the queues provided in the question, whether that is "could", "can", "may be", etc, and answer the question accordingly.

    -Jud

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    jnorton1547 Junior | Next Rank: 30 Posts Default Avatar
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    Post Thu Feb 07, 2013 8:38 am
    nada?

    Post Thu Feb 07, 2013 9:56 am
    This is a really excellent question, and it points out some of the ways that interpreting the GMAT can be tricky.

    In your first example, "can the positive integer a be written as the sum of two different prime numbers," let's think about what would happen if we interpreted that as "can some a, at some time..." If a=12, that could be written as 5 + 7. If a=4, though, there's no way to express it as a sum of two different primes. So we'd already have an answer - yes, it can for some values of a, but not for others. We wouldn't even need the statements here! The GMAT will never give you a situation where the question itself is sufficient to answer the question, even without any statements, so we must be missing something.

    The question specifically says "can the positive integer a..." This means that "a" represents a single value. To know if it's expressible as the sum of primes, we either need to know what "a" is, or know enough information about it to definitively answer the question. The statements will tell us one of three things:
    1) yes, it's expressible as the sum of two primes (sufficient)
    2) no, it definitely isn't expressible as the sum of two primes (sufficient)
    3) maybe - it's possible that it is or isn't (insufficient)

    It's not really the "can" that dictates the "always" aspect, as you said. It's the fact that the question makes clear that we're looking for a specific value of x.
    "Can there be a value of 'a' for which this is true?" would be a "sometimes" question. The question "can" is asking about what 'a' could be.
    "Can 'a' be expressed as a particular thing?" is an "always" question. The question "can" is asking about the properties of a specific value of 'a.'

    In your second example, we don't have a specific variable or a specific average that we're talking about. We're just talking about any average of a consecutive set. When the question asks "which of the following could be true?" it means that there are usually 2 options:
    1) sometimes true and sometimes not (correct)
    2) never true (incorrect)
    Occasionally you might also get an "always true," but that's more rare. Your job in these Roman Numeral questions with "could be" is to try to find an instance where the statement is true. You don't have to prove that it's true every time.

    *Make sure you distinguish between these and the Roman Numeral questions that ask "which of the following MUST be true?" In those cases, you will need to prove that it's true every time.

    There is a distinction between the kinds of information that DS and PS ask about (because DS is about sufficiency, it tends toward yes/no answers, while PS is a better format for asking about possibilities. The "which of the following could be" language will only be found in PS).

    I think that the distinction between these is less about DS v. PS, though, and more about the way they define what's being asked about. If we're looking at a specific entity "the positive integer a," we'll need a definitive "yes" or "no." If we're asked "which of the following COULD be," we're only looking for a "maybe."

    Did that answer your question?

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    jnorton1547 Junior | Next Rank: 30 Posts Default Avatar
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    Post Thu Feb 07, 2013 10:43 am
    To everything I asked before, yes, it answered my questions. And very well too. Thank you. The wait was worth it!

    But I do have one more question - or really a matter of clarification - that spawned from your answer:

    So in latching on to "the" in the question stem of the first example to determine that it's asking for a single value, and to follow that up with the stating that the distinction is less about "can" vs "always" and more about what the question is asking for, does this mean that there may be times when a DS question uses less definitive language in the question stem, and that we may need to approach it with "can this work" rather than "does this always lead to..."?

    So in using a variation of this example, will there ever be a situation where the question asks "Can a positive integer 'a' be written as the sum of two different prime numbers?"[/u]

    Post Mon Feb 11, 2013 4:54 pm
    No, a DS question will never ask you effectively "is there some integer 'a' that can be written as..." (I actually flipped through all of OG13 just to double-check that there were no exceptions out there!)

    The reason is this: "is there some integer" questions, like the one we have here, are generally questions we could answer without any extra information provided. "Is there some number that's an even multiple of 3?" Sure, lots of them! No other information needed. So with DS, it makes sense that they ask "Is the integer 'n' an even multiple of 3?" Now we need some more information about 'n' before we can answer this.

    DS will always ask you about a specific value, specific average, specific ratio, etc. That doesn't necessarily mean that you have to determine the value to answer the question, though! Consider:

    Is the integer 'x' between 29 and 34?

    (1) x is a multiple of 7

    Here, we don't need to pinpoint which multiple of 7 'x' is. It's enough to know that there aren't any multiples of 7 in the range 29 to 34. But theoretically at least, 'x' does have a singular value.

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    jnorton1547 Junior | Next Rank: 30 Posts Default Avatar
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    Post Mon Feb 11, 2013 5:11 pm
    Wow, awesome! Thank you so much for checking the OG for me!

    I figured that was the case - I couldn't think of a way for a DS question to ask it that way, but I'm not a test maker so I'm sure there are plenty of ways I can't think of asking some of these questions!

    I appreciate your diligence in both flipping through the OG and in your explanations. Very helpful!

    Post Wed Feb 13, 2013 9:11 am
    My pleasure! I wanted to double-check for my own sake, in case any of my students asks this question again. Good luck with your studies!

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