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Traveling In A Triangle of Points

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by EOV » Thu Nov 29, 2012 10:40 am
Hi everybody,

John is trying to get from point A to point C, which is 20 miles away directly to the northeast; however the direct road from A to C is blocked and John must take a detour. John must travel due north to point B and then drive due east to point C. How many more miles will John travel due to the detour than if he had traveled the direct 20 mile route from A to C?

(1) The ratio of the distance going north to the distance going east is 4 to 3
(2) The distance traveled north going the direct route is 16

(A) Statement (I) ALONE is sufficient, but statement (II) alone is not sufficient
(B) Statement (II) ALONE is sufficient, but statement (I) is not sufficient
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
(D) Each statement ALONE is sufficient
(E) Statements (I) and (II) TOGETHER are NOT sufficient

Correct answer (?)
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Source: — Data Sufficiency |
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by Bill@VeritasPrep » Thu Nov 29, 2012 10:56 am
The question sets up a right triangle for us, with the route north from A to B and the route east from B to C being the legs, and the direct route from A to C being the hypotenuse. We know the distance of the hypotenuse, so all we need is either AB or BC to be able to find the difference in distance.

S1 tells us that we have a 3/4/5 triangle, so we can easily determine AB and BC. Sufficient.

S2 tells us that AB is 16, which will allow us to find BC by using the Pythagorean theorem. Sufficient.
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by mamathak » Wed Apr 03, 2013 3:13 am
on what basis can we assume that ABC is a right angle triangle. John would have travelled too less or too more due north either reducing AB or increasing AB to an extent that it is not right triangle?
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by GMATGuruNY » Wed Apr 03, 2013 8:54 am
mamathak wrote:on what basis can we assume that ABC is a right angle triangle. John would have travelled too less or too more due north either reducing AB or increasing AB to an extent that it is not right triangle?
Due north from A to B implies vertical distance: |
Due east from B to C implies horizontal distance: --->
Thus, if John travels due north from A to B and then due east from B to C, AB and BC will form a right angle:

B ------->C
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