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GMAT Practice exam 2 - Word Problem/geometry

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by GMATGuruNY » Sun Jun 26, 2016 5:03 am
On an aerial photograph, the surface of a pond appears as circular region of radius 7/16 inch. If a distance of 1 inch on the photograph corresponds to an actual distance of 2 miles, which of the following is the closest estimate of the actual surface area of the pond, in square miles?

A. 1.3
B. 2.4
C. 3.0
D. 3.8
E. 5.0
Convert the given radius into miles.
Since 1 inch on the photograph is the equivalent of 2 miles, we get:
(7/16 inches) * (2 miles)/(1 inch) = 7/8 miles.

Area of the pond = πr² ≈ (22/7)(7/8)² = (22*7)/8² = 154/64 = between 2 and 3.

The correct answer is B.
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by OptimusPrep » Sun Jun 26, 2016 10:06 am
lucas211 wrote:Hello BTG

Having some issues conceptualizing this problem - the best approach.
Could anyone assist?

On an aerial photograph, the surface of a pond appears as circular region of radius 7/16 inch. If a distance of 1 inch on the photograph corresponds to an actual distance of 2 miles, which of the following is the closest estimate of the actual surface area of the pond, in square miles?

A. 1.3
B. 2.4
C. 3.0
D. 3.8
E. 5.0

Thanks in advance
Radius on the photograph = 7/16 inch
Actual radius = (7/16)*2 miles = 7/8miles.

Area of the pond = pi*(7/8)^2 = (22/7)*(7/8)*(7/8) = 22*7/64 = 7/3 approximately.
{We can estimate 22/64 as 22/66 = 1/3}

Correct option: B
Is there any particular part you are having problems with?
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by Jeff@TargetTestPrep » Tue Jan 02, 2018 10:57 am
lucas211 wrote:On an aerial photograph, the surface of a pond appears as circular region of radius 7/16 inch. If a distance of 1 inch on the photograph corresponds to an actual distance of 2 miles, which of the following is the closest estimate of the actual surface area of the pond, in square miles?

A. 1.3
B. 2.4
C. 3.0
D. 3.8
E. 5.0
We can create a proportion in which n is the radius of the pond in miles:

1/2 = (7/16)/n

n = 2(7/16)

n = 7/8

Thus, the area of the pond is (7/8)^2 x π. Recall that the fractional approximation of π is 22/7. Thus, we have:

(7/8)^2 x π ≈ 49/64 x 22/7 = 7/32 x 11/1 = 77/32 = 2 13/32 ≈ 2 12/30 = 2 2/5 = 2.4

Answer: B

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