Practice GMAT Data Sufficiency Question
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John is trying to get from point A to point C, which is 15 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 15 mile route from A to C?
 Tha ratio of the distance going north to the distance going east is 4 to 3
 The distance traveled north going the direct route is 12
Correct Answer: D
 Draw a diagram of the problem with the information from the question:
AC = 15
You are dealing with a righttriangle since a right angle will be formed by going straight north and then turning straight east. 
Evaluate Statement (1) alone.
 Translate the information from Statement (1) into algebra:
(AB)/(BC) = 4/3
3(AB) = 4(BC)  Set up a Pythagorean theorem equation:
(AB)^{2} + (BC)^{2} = (AC)^{2}
(AB)^{2} + (BC)^{2} = (15)^{2}  You now have two equations and two unknowns:
Equation (1): (AB)^{2} + (BC)^{2} = (15)^{2}
Equation (2): 3(AB) = 4(BC)  With two unique equations and two unknowns, a solution must exist. With this solution, you can subtract 15 from the detour distance and arrive at an answer.
 Statement (1) is SUFFICIENT.
 Note: You should not do these calculations on the test since they are not necessary for determining sufficiency. However, to demonstrate that there is a solution, we show how you would arrive at a numerical answer:
(AB)^{2} + (BC)^{2} = (15)^{2}
(AB)^{2} + (.75AB)^{2} = (15)^{2}
{rearrange Equation 2, solving for BC and substitute in BC=.75AB}
(AB)^{2}(1 + .75^{2}) = 225 {factor out (AB)^{2}}
(AB)^{2} = 144
AB = 12
Substitute Back into Equation 2:
3(12) = 4(BC)
BC = 9  With these two distances, you can calculate the distance traveled on the detour.
Direct Route: 15
Detour: 9 + 12 = 21
Extra Distance: 21  15 = 6
 Translate the information from Statement (1) into algebra:

Evaluate Statement (2) alone.
 Set up a Pythagorean theorem equation:
(AB)^{2} + (BC)^{2} = (AC)^{2}
(AB)^{2} + (BC)^{2} = (15)^{2}  You are told that AB = 12. Substitute this information in and solve for BC.
(12)^{2} + (BC)^{2} = (15)^{2}
(BC)^{2} = 81
BC = 9  Statement (2) is SUFFICIENT.
 Note: You should not do these calculations on the test since they take up time and are not necessary for determining sufficiency. However, to demonstrate that there is a solution, we show how you would arrive at a numerical answer:
Direct Route: 15
Detour: 9 + 12 = 21
Extra Distance: 21  15 = 6
 Set up a Pythagorean theorem equation:
 Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT, answer D is correct.
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