Hi All,
While the answer choices appear "close together", the way that the prompt is written allows for a great estimation "shortcut" that you can take advantage of. You do still need to do some algebra though....
We're asked to compare HALF the circumference of a circle to the diameter of a circle, so let's deal with THAT comparison first....
Circumference = 2(pi)R
HALF a Circumference = (pi)R
Diameter = 2R
We're told that a runner moves at a constant speed and that the difference between running (pi)R units and 2R units is 4 minutes (we're never told what the units are, but that doesn't matter). Here we have the equation:
pi(R) - 2R = 4 minutes
We're asked to figure out how long it takes to run the DIAMETER, so we're looking for the value of 2R.
I'm going to 'factor out' the R from the above equation:
R(pi - 2) = 4
Since pi = approximately 3.14, we now have.....
R(3.14 - 2) = 4
R(1.14) = 4
Without doing the exact calculation, I can see that R is BETWEEN 3 (which is too small) and 4 (which is too big).
If R = 3 EXACTLY, then 2R = 6 minutes
If R = 4 EXACTLY, then 2R = 8 minutes
I know that 6 is too SMALL and 8 is too BIG, so the answer has to be BETWEEN 6 and 8. There's only one answer that fits...
Final Answer:
GMAT assassins aren't born, they're made,
Rich