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Which is closest to zero?

This topic has 4 expert replies and 2 member replies
BlueDragon2010 Senior | Next Rank: 100 Posts Default Avatar
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Which is closest to zero?

Post Thu Feb 27, 2014 2:40 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])


    Of the four number represented on the number line above, is r closest to zero?

    (1) q = -s

    (2) -t < q

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    Post Thu Feb 27, 2014 2:54 pm
    In short, the 1st statement guarantees that 0 is half-way between q and s, so r must be the closest to 0. I go through the question in detail in the full solution below (taken from the GMATFix App).

    ttp://www.youtube.com/watch?v=XDj5Nd4tjOU" target="_blank">

    -Patrick

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    Last edited by Patrick_GMATFix on Thu Feb 27, 2014 2:56 pm; edited 1 time in total

    Post Thu Feb 27, 2014 2:55 pm
    Quote:
    ttp://postimg.org/image/uvwmxp3wn/" target="_blank">
    Of the four numbers represented on the number line, is r closest to zero?

    (1) q = -s
    (2) -t < q
    Target question: Is r closest to zero?

    Statement 1: q = -s
    This tells us that q and s are on opposite sides of zero (i.e., one is positive and one is negative) AND it tells us that q and s are the same distance from zero.
    So, we get something like this: q.....0.....s
    Since r is between points q and s, r must be the closest point to zero
    Since we can answer the target question with certainty, statement 1 is SUFFICIENT

    Statement 2: -t < q
    There are several sets of values that satisfy this condition. Here are two:
    Case a: q = -1, r = 0, s = 1 and t = 2, in which case r IS the closest to zero
    Case b: q = 0, r = 1, s = 2 and t = 3, in which case r is NOT the closest to zero
    Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

    Answer = A

    Cheers,
    Brent

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    GMAT/MBA Expert

    Post Thu Feb 27, 2014 3:02 pm
    BlueDragon2010 wrote:


    Of the four number represented on the number line above, is r closest to zero?

    (1) q = -s

    (2) -t < q
    Dear BlueDragon2010,
    I'm happy to help with this. Smile

    Remember, of course, diagrams are not necessarily drawn to scale in GMAT DS. SEe
    http://magoosh.com/gmat/2012/gmat-trick-drawn-as-accurately-as-possible/

    Statement #1:
    If q = -s, then zero must be the midpoint of the segment from q to s. Well, even if the diagram is not to scale, any point between q & s will be close to the midpoint than either q or s would be. Thus, r must be closest to zero. This answer gives a very clear answer, so this statement is sufficient.

    Statement #2:
    -t < q. Well, let's just consider the points evenly spaced. It could be that q = -1, r = 0, s = 1, and t = 2 --- then, this inequality would be true. It could also be that q = 1, r = 2, s = 3, and t = 4, and this inequality would still be true. Even more possibilities emerge when we consider that the points might not be evenly spaced, because the diagram is not necessarily drawn to scale. With the two choices we made so far, r was closest to zero in one, and q was closest to zero in another. With uneven choices, we could also make s the one closest to zero. This statement allows for different configurations that result in different answer to the prompt question. This statement, along and by itself, is not sufficient.

    Answer = (B)

    Does all this make sense?
    Mike Smile

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    Post Fri Feb 28, 2014 6:40 am
    Mike@Magoosh wrote:
    Remember, of course, diagrams are not necessarily drawn to scale in GMAT DS. SEe
    http://magoosh.com/gmat/2012/gmat-trick-drawn-as-accurately-as-possible/
    Be sure to note Mike's advice. When it comes to Geometry questions on the GMAT, there are assumptions we CAN make and there are others we CANNOT make.

    If you're interested, we have a free video that covers all of this: http://www.gmatprepnow.com/module/gmat-geometry?id=863

    Cheers,
    Brent

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    Use our video course along with Beat The GMAT's free 60-Day Study Guide

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    Come see all of our free resources

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    divyasood11 Junior | Next Rank: 30 Posts Default Avatar
    Joined
    30 Nov 2014
    Posted:
    13 messages
    Post Sun Dec 14, 2014 9:52 am
    Hi Mike
    can you suggest a strategy which makes it easy and quick to come up with such sets of numbers quickly during the test

    Thank You

    Post Sun Dec 14, 2014 12:30 pm
    Hi divyasood11,

    When you choose to TEST VALUES on DS questions, you have to focus on the "thoroughness" of your examples. DS questions often come with "restrictions" that you have to account for and the specific question that is asked often focuses on a specific idea that should help you to further measure the thoroughness of your work.

    As a general rule, you want to use small, simple values (-3, -2, -1, 0, 1, 2, 3, etc.)...unless something in the prompt clues you in to do otherwise.

    Here, we're first restricted by the picture. Since we're dealing with a number line, we know that Q < R < S < T. 4 variables is A LOT, so you really should focus on simple values. Now, consider the possibilities:

    all positive
    all negative
    0 could be in there
    a mix of positives, 0 and negatives is possible

    Next, we have the question: "Is R closest to zero?"

    If Q, S or T is actually 0, then the answer is NO.
    If Q, S or T is closer to 0 than R, then the answer is NO.
    If R actually is closer than both Q and S, then we'll know that it's closer than T, so the answer would be YES.

    Once you get down to the two Facts, additional restrictions show up. As a general rule, I choose values first for the variables that I know the most about.

    In Fact 1, Q = -S

    This means that Q and S are OPPOSITES (and neither can be 0). From the number line, we know that Q < S, so Q MUST be negative and S MUST be positive. After making these deductions, what values would YOU choose for Q and S? Now, since R is somewhere between Q and S, what COULD you choose for R?

    With enough practice, all of these steps will become natural (and faster). This type of work requires lots of note-taking though, so you should NEVER do this work in your head.

    GMAT assassins aren't born, they're made,
    Rich

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