Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
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 1.0022? Look at 1.002 as 1 + 0.002. So what is (1 + 0.002)2?
We get (1 + 0.002)(1 + 0.002) = 12 + 0.002×1 + 1×0.002 + 0.0022. Notice that the last term is very, very small: 0.0022 = 0.000004. So we can ignore this part, since we are only going to round to 3 decimal places.
We get (1 + 0.002)(1 + 0.002) ≈ 12 + 0.002×1 + 1×0.002 = 1.004.
Now multiply by another 1.002.
1.004 × 1.002 = (1 + 0.004)(1 + 0.002) = 12 + 0.004×1 + 1×0.002 + 0.004×0.002. Again, we can ignore the last bit, because it’s so small.
1.004 × 1.002 ≈ 12 + 0.004×1 + 1×0.002 = 1.006.
Finally, multiply by one last 1.002, rounding the same way as we go:
1.006 × 1.002 ≈ 12 + 0.006×1 + 1×0.002 = 1.008.
The correct answer is C.