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Number Line Data Sufficiency

Expert replies
by Mustcrackgmat » Fri Dec 20, 2013 12:13 pm
A---B---C---D

In the figure above, is CD > BC ?
(1) AD = 20
(2) AB = CD

According to me the answer was B. But the correct answer is E.

Can someone please help me how to get to the correct answer! Thanks!
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Source: — Data Sufficiency |

by ceilidh.erickson » Fri Dec 20, 2013 12:33 pm
On number line problems, you can never assume that points on a number line are evenly spaced unless you are EXPLICITLY told.

Is CD > BC ?
The question itself implies that we can't treat these points as evenly spaced. We're asking if 2 of the points are farther apart than 2 of the other points.

(1) AD = 20
The distance between the 2 farthest points does not allow us to compare the distances between the points in between. One possibility:

0--2--------------17-----20

Or it could be:

0-1-2--------------------20

Insufficient.

(2) AB = CD
Once again, knowing that the distances between these sets of points are equal doesn't tell us anything about the distance from B to C. One possibility is that they're all equidistant:

0--2--4--6

Or, perhaps B and C are much farther apart than A and B or C and D:

0--2---------------10--12

Insufficient.

When we put the statements together, be still don't have enough information to determine the relative distance between B and C.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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by Mustcrackgmat » Fri Dec 20, 2013 9:22 pm
I thought "AD=20" or "AB=CD" meant the product of these two numbers on the line (A*D=20 or A*B=C*D)!! How could have I distinguished!
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by Stuart@KaplanGMAT » Fri Dec 20, 2013 11:18 pm
Mustcrackgmat wrote:I thought "AD=20" or "AB=CD" meant the product of these two numbers on the line (A*D=20 or A*B=C*D)!! How could have I distinguished!
Hi!

In geometry, whenever two points are put together like that, they always describe the line formed by connecting them. The same rule applies to number lines, which are really just a form of linear geometry.
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Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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