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?
  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
Correct Answer: D
  1. Draw a diagram of the problem with the information from the question:
    Figure 1
    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.

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