Compound Interest - Algebra

[Sage Pearce-Higgins]

I encourage you to hone your detective skills and look out for clues on GMAT problems. One such clue here is that the answers contain variables: this opens up the way for the strategy of smart numbers. Since we don't know (and can't ever find out) what "x" is in this problem, we're free to pick any value for x. Let's pick an easy number to work with, say 10, and see what happens.

If x = 10, then, after 1 year, Maria will receive $100 dollars if the interest is compounded annually. However, if the interest is compounded semi-annually, then she'll get 5% interest after after 6 months - that's $50 - and then that $50 will be reinvested, so that after 12 months she'll get 5% more interest, but this time on $1050. Using a convenient % benchmark, 1% of 1050 is 10.5, so 5% is 52.5. So, after a year, Maria will have received a total of $102.5 interest. Using this smart number of 10, Maria has received $2.5 more interest for the 'compounded semiannually' investment.

To finish the problem, we need to plug our smart number into the answer choices to see which one gives us $2.5:
A 5x10 = 50 too big
B 10x10 = 100 too big
C 100/20 = 5 too big
D 100/40 = 2.5 that works
E 100 + ... = too big

Check out the FDP and Algebra strategy guides for more on smart numbers.

One final point about guessing on this problem: you can see that 'compounded semiannually' simply means that the interest after 6 months is reinvested, making it only slightly more profitable. Once you're familiar with that, then answers A, B, and E look too large to be possible.