FDP Problem (OG PS #174)

Hi mattnyc15,

I'm going to point out an error that you made so that you can reattempt this question:

10^4 = 10,000
10^2 = 100

10^4 - 10^2 is NOT 10^2

If you do that subtraction correctly, you can then take advantage of how the answer choices are 'spread out' and actually estimate the correct answer.

GMAT assassins aren't born, they're made,
Rich

Be careful! You can't simply subtract the exponents when you're subtracting 10^4 - 10^2. Those actual numbers would be 10,000 - 100, which would yield 9,900, not 100.

If you simplified to 9,900, though, you'd still have trouble coming up with an answer. You would be multiplying an integer by a non-terminating decimal, so the answer would go on forever!

Look at the answer choices: they're (almost) all relatively simple, terminating answers. That's our clue that there's a simpler way of solving than doing long multiplication. Since 10^4 and 10^2 are powers of 10, that should trigger us to this about DECIMAL PLACEMENT.

If we distribute, the 10^4 shifts the decimal 4 places, and the 10^2 shifts the decimal 2 places:
12.12 - 0.12 (assume the bars are above and not below)

Since both contain the 0.12, when we subtract we get rid of the decimal entirely, and are left with 12.

Jinx! Rich and I posted the same thing at almost exactly the same moment. Great minds...