­A satellite is currently in a circular orbit with radius 32,714km

Despite what GMAC has claimed about plane geometry not appearing on the GMAT Focus, this new GMAT Focus question from the official practice exams clearly requires one to know the formula for the circumference of a circle, C = 2(pi)r.  

2(pi) = about 6, so just multiply the number in each column by 6 to arrive at the correct answers.  

Hi MartyMurray, could you please help explain how we can approach this problem?

­A satellite is currently in a circular orbit with radius 32,714 km about the center of the earth.

Select for 0.5 km the increase, to the nearest whole kilometer, in the distance the satellite travels about the center of the earth during each revolution if the orbital radius of the satellite is increased by 0.5 km. And select for 1.5 km the increase, to the nearest whole kilometer, in the distance the satellite travels about the center of the earth during each revolution if the orbital radius of the satellite is increased by 1.5 km. Make only two selections, one in each column.­

According to GMAC, Geometry does not appear on the Focus Edition, but questions, such as this one, on the official practice tests indicate that knowing some basic Geometry concepts that can be considered common knowledge is necessary for getting some Quant questions correct.

Among those concepts are the Pythagorean theorem and formulas for calculating the areas of basic shapes including rectangles, triangles, and circles.

Now, this question requires use of the formula for the circumference of a circle, which is \(C = 2πr = πd\). where \(C\) is the circumference, \(r\) is the radius, \(d\) is the diameter of the circle, and the value of \(π\) is approximately \(3.14\).

Given that formula, we can see that, any time we increase the radius of a circle, we increase the circumference of the circle by \(2π\) times the increase in the radius, or by about \(6.28\) times the increase in the radius.

So, to calculate the increase in the distance the satellite travels during each revolution, we can ignore the figure 32,714 and just multiply each increase in the radius by 6.28.

If the radius is increased by 0.5 km, the distance is increased by approximately 0.5 × 6.28 = 3.14, which rounded to the nearest whole kilometer is 3.

If the radius is increased by 1.5 km, the distance is increased by approximately 1.5 × 6.28 = 9.42, which rounded to the nearest whole kilometer is 9.

3km

9km

27km

81km

150km

450km

Correct answer: 3km, 9km­