# Practice GMAT Data Sufficiency Question

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?
1. Tha 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 12
 A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
1. Draw a diagram of the problem with the information from the question: AC = 15
You are dealing with a right-triangle since a right angle will be formed by going straight north and then turning straight east.
2. Evaluate Statement (1) alone.
1. Translate the information from Statement (1) into algebra:
(AB)/(BC) = 4/3
3(AB) = 4(BC)
2. Set up a Pythagorean theorem equation:
(AB)2 + (BC)2 = (AC)2
(AB)2 + (BC)2 = (15)2
3. You now have two equations and two unknowns:
Equation (1): (AB)2 + (BC)2 = (15)2
Equation (2): 3(AB) = 4(BC)
4. 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.
5. Statement (1) is SUFFICIENT.
6. 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 + .752) = 225 {factor out (AB)2}
(AB)2 = 144
AB = 12
Substitute Back into Equation 2:
3(12) = 4(BC)
BC = 9
7. 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
3. Evaluate Statement (2) alone.
1. Set up a Pythagorean theorem equation:
(AB)2 + (BC)2 = (AC)2
(AB)2 + (BC)2 = (15)2
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
3. Statement (2) is SUFFICIENT.
4. 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
4. Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT, answer D is correct.