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Apr 2808:00 AM PDT
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Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
22 Jun 2022, 02:00
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63% (02:04) correct
38%
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Once a month, a crop duster sprays a triangular area defined by three farm houses—A, B, and C—as indicated in the figure above. Farmhouse B lies due west of Farmhouse C. Given the compass directions and distances (in miles) indicated in the figure, what is the total area that the crop duster sprays?
(1) Farmhouse C is located 4 miles further south than farmhouse A.
(2) Farmhouse C is located 10 miles further east than farmhouse A.
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22 Jun 2022, 02:49
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(1) Farmhouse C is located 4 miles further south than farmhouse A.
With this information we can create a new point, and with it a secondary triangle. Let the new point be H. Now AHB is a new right angle triangle with a hypotenuse of 5, and a height of 4. This means that the distance from H to B is 3, as 5-4-3 is a Pythagorean triplet. This also creates a bigger triangle, AHC, with a height of 4 and a base of 10.
The area of ΔABC = \(areaΔAHC - areaΔAHB\)
Area of ΔAHC: \(\frac{10*4}{2} = 20\)
Area of ΔAHB: \(\frac{4*3}{2} = 6\)
Area of ΔABC: \(20 - 6 = 14\)
SUFFICIENT
(2) Farmhouse C is located 10 miles further east than farmhouse A.
Similarly as above, this statement provides information to create the same triangles. The only difference being that now one is told that line HC = 10, which means that HB = 3. This means that AH = 4 due to the Pythagorean triplet of 5-4-3. With this one can do the exact same calculations as above to solve for the area of ΔABC.
SUFFICIENT
Answer D
With this information we can create a new point, and with it a secondary triangle. Let the new point be H. Now AHB is a new right angle triangle with a hypotenuse of 5, and a height of 4. This means that the distance from H to B is 3, as 5-4-3 is a Pythagorean triplet. This also creates a bigger triangle, AHC, with a height of 4 and a base of 10.
The area of ΔABC = \(areaΔAHC - areaΔAHB\)
Area of ΔAHC: \(\frac{10*4}{2} = 20\)
Area of ΔAHB: \(\frac{4*3}{2} = 6\)
Area of ΔABC: \(20 - 6 = 14\)
SUFFICIENT
(2) Farmhouse C is located 10 miles further east than farmhouse A.
Similarly as above, this statement provides information to create the same triangles. The only difference being that now one is told that line HC = 10, which means that HB = 3. This means that AH = 4 due to the Pythagorean triplet of 5-4-3. With this one can do the exact same calculations as above to solve for the area of ΔABC.
SUFFICIENT
Answer D
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