Manhattan GMAT Challenge Problem of the Week – 16 Aug 2011:
Here is a new Challenge Problem! If you want to win prizes, try entering our Challenge Problem Showdown. The more people that enter our challenge, the better the prizes!
Rounded to three decimal places, =
If you were a computer (or had access to one), you could mechanically take 1.002 to the fourth and then round. However, by hand that would take way too long. The key to this problem is to try a smaller power of 1.002 first.
What is ? Look at 1.002 as 1 + 0.002. So what is ?
We get . Notice that the last term is very, very small: . So we can ignore this part, since we are only going to round to 3 decimal places.
We get .
Now multiply by another 1.002.
. Again, we can ignore the last bit, because it’s so small.
Finally, multiply by one last 1.002, rounding the same way as we go:
The correct answer is C.
Special Announcement: If you want to win prizes for answering our Challenge Problems, try entering our Challenge Problem Showdown. Each week, we draw a winner from all the correct answers. The winner receives a number of our our Strategy Guides. The more people enter, the better the prize. Provided the winner gives consent, we will post his or her name on our Facebook page.