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27 Oct 2020, 06:00
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
39% (01:54) correct
61%
(02:20)
wrong
based on 147
sessions
History
Date
Time
Result
Not Attempted Yet
\(K=1.03^N\), N is a positive integer, what is the least possible value of N that will make K be greater than 2.
A. 21
B. 22
C. 23
D. 24
E. 25
A. 21
B. 22
C. 23
D. 24
E. 25
27 Oct 2020, 09:23
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Really we're asking: if we earn 3% over and over again (so we multiply our investment by 1.03 many times), how many times will we need to apply that interest rate to double our money?
I don't think there's any practical way to answer that question with pen and paper. I'd imagine, especially seeing the numbers in the problem, that this is testing something called the "Rule of 72", that says, when you compound an x% interest rate, you'll double your money if you apply interest roughly 72/x times. Using that here, we'd find it will take roughly 72/3 = 24 applications of the interest rate to double our money, so the answer is roughly 24.
There are three problems though: the Rule of 72 only provides an estimate. To pick the right answer to this question, you need to know how good the estimate is, and whether it produces an answer slightly too large or slightly too small. No one taking the GMAT is expected to even know a rule like this, let alone how good an estimate it produces. And it's a rule proven using logarithms, so there's absolutely no way a test taker could figure it out on the spot.
The answer here is indeed 24, but I worked that out with a calculator. I suppose there might be an alternative method using something like the binomial theorem, but at a glance that looks like it would take an hour, so I haven't tried it (and would be well beyond the scope of the GMAT in any case).
I don't think there's any practical way to answer that question with pen and paper. I'd imagine, especially seeing the numbers in the problem, that this is testing something called the "Rule of 72", that says, when you compound an x% interest rate, you'll double your money if you apply interest roughly 72/x times. Using that here, we'd find it will take roughly 72/3 = 24 applications of the interest rate to double our money, so the answer is roughly 24.
There are three problems though: the Rule of 72 only provides an estimate. To pick the right answer to this question, you need to know how good the estimate is, and whether it produces an answer slightly too large or slightly too small. No one taking the GMAT is expected to even know a rule like this, let alone how good an estimate it produces. And it's a rule proven using logarithms, so there's absolutely no way a test taker could figure it out on the spot.
The answer here is indeed 24, but I worked that out with a calculator. I suppose there might be an alternative method using something like the binomial theorem, but at a glance that looks like it would take an hour, so I haven't tried it (and would be well beyond the scope of the GMAT in any case).
General Discussion
11 Sep 2025, 05:02
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