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Number line intervals

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by GmatGreen » Wed Jan 15, 2014 7:33 am
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If the successive tick marks shown on the number line above are equally spaced and if x and y are the numbers designating the end points of intervals as shown, what is the value of y?

1) x = 1/2

2) y-x = 2/3
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Source: — Data Sufficiency |
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by Patrick_GMATFix » Wed Jan 15, 2014 7:40 am
Think of the length of each interval as a constant (k) and you will be able to derive equations to prove sufficiency from each statement. The solution below is taken from the GMATFix App.

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by Matt@VeritasPrep » Wed Jan 15, 2014 11:46 am
One tip on this question: many students miss this because they interpret the statements as saying x is 1/2 of something, and feel like the statements are insufficient because that half is undefined ("x is half of WHAT?"). But Statement 1 simply says x = .5 -- the number, .5 -- and with that the question is much easier to solve.

For instance, take the first statement. We know x is three tick intervals from 0. The intervals all have the same length, so let's call that length t. Now we know that the distance from 0 to x, or (x - 0), is 3t.

With that, we can write the equation x = 3t, substitute .5 for x, and find that t = (.5)/3, or t = 1/6.

From there, we note that y - 0 = 7t, so y = 7 * (1/6), or 7/6. SUFFICIENT!

A similar strategy works for S2. Hope that helps!
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