Manhattan GMAT Challenge Problem of the Week - 16 Aug 2011

by Manhattan Prep, Aug 16, 2011

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Question

Rounded to three decimal places, [pmath]1.002^4[/pmath] =

A. 1.004

B. 1.006

C. 1.008

D. 1.012

E. 1.016

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 [pmath]1.002^2[/pmath]? Look at 1.002 as 1 + 0.002. So what is [pmath](1 + 0.002)^2[/pmath]?

We get [pmath](1 + 0.002)(1 + 0.002) = 1^2 + 0.002*1 + 1*0.002 + 0.002^2[/pmath]. Notice that the last term is very, very small: [pmath]0.002^2 = 0.000004[/pmath]. So we can ignore this part, since we are only going to round to 3 decimal places.

We get [pmath](1 + 0.002)(1 + 0.002) approx 1^2 + 0.002*1 + 1*0.002 = 1.004[/pmath].

Now multiply by another 1.002.

[pmath]1.004*1.002 = (1 + 0.004)(1 + 0.002) = 1^2 + 0.004*1 + 1*0.002 + 0.004*0.002[/pmath]. Again, we can ignore the last bit, because its so small.

[pmath]1.004*1.002 approx 1^2 + 0.004*1 + 1*0.002 = 1.006[/pmath].

Finally, multiply by one last 1.002, rounding the same way as we go:

[pmath]1.006*1.002 approx 1^2 + 0.006*1 + 1*0.002 = 1.008[/pmath].

The correct answer is C.

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