In this month’s “brain teaser,” we present an official GMAT question. While thinking about this question, it’s critical to remember/understand that the GMAT does not allow a calculator on the Quantitative Section, so this question must be able to be solved without tedious calculation. In fact, this one can be solved without writing anything down!
An investment of $1000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $1000 increased to $4000 by earning interest. In how many years after the initial investment was made the $1000 have increased to $8000 by earning interest at that rate?
A. 16
B. 18
C. 20
D. 24
E. 30
Answer:
This “brain teaser” is actually an official GMAT question, and it is a great one! The first thing to recognize is that the test writers can’t possibly expect you to fully calculate this out using the compound interest formula. That is way too much math!!! Even with a four function calculator like the one that you have on the GRE, it would still be too tedious and time consuming. So there MUST be a shortcut! The key to really solving this is to think about what the question is really asking for. Essentially you are being asked how long it would take for the investment to double from $4,000 to $8,000. Hmm? Well have they given us any information relative to how long it took the investment to double so far? Yes! If the investment started at $1,000, it then doubled to $2,000 and then doubled again to $4,000. And it took 12 years for that to happen, so 6 years for it to double each time. Therefore it should take 6 more years for the investment to double again to $8,000. Thus, the answer is 18, choice B!