If $1,000 is deposited in a certain bank account and remains in the account along with any accumulated interest, the dollar amount of interest, I, earned by the deposit in the first n years is given by the formula

I = 1,000 ( (1 + r/100)^n - 1 ),

where r percent is the annual interest rate paid by the bank. Is the annual interest rate paid by the bank greater than 8 percent?

(1) The deposit earns a total of $210 in interest in the first two years.
(2) ( 1 + r/100 )^2 > 1.5


The corrrect answer is A.

I got D. Why is (2) not sufficient? Any help is appreciated.

My understanding is that choice II gives you the formula for n=3 and not n=2 (two years) that our question asks for.

the way you've written (2) it is definitely sufficient, so i suggest that you go back and proofread.
to wit:
(1 + r/100)^2 > 1.5
means
1 + r/100 > √1.5, which is between 1.2 and 1.3 (because 1.2 is √1.44 and 1.3 is √1.69)
so
1 + r/100 is definitely bigger than 1.2
so
r/100 is definitely bigger than 0.2
so
the interest rate is more than 20%/year
sufficient.

look for transcription mistakes: did you write '>' instead of '<' ? did you write 1.5 instead of 1.05? etc.

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also, just for completeness, i should add that the best way to realize that #1 is sufficient is to realize that it will provide an EQUATION THAT ALLOWS YOU TO SOLVE for the interest rate. you don't even have to set up the equation to figure this out: a moment's reflection will tell you that there must be one, and only one, interest rate that will return exactly $210 (any higher rate will return more, and any lower rate will return less). since there is a unique rate, it's automatically sufficient to answer the question.

statement 2 should be ( 1 + r/100 )^2 > 1.15

solution to this question should be A

square root of 1.15 is between 1.07 and 1.08. Let's say it is 1.075.
This means that r/100 > 0.075
hence r > 7.5
This is still insufficient as r could be 7.6, 7.7 etc.
hence answer is A.

Okay - so there was a typo when you posted originally and the number should've been 1.15, not 1.5, in statement 2. That's what Ron was saying - there was something wrong with the problem as written b/c the answer was reported as A, yet statement 2 as written was sufficient.

As viksnme pointed out, statement 2 tells us that it could be greater than 8% but it could also be in the high 7% range... so we can't tell.

If you're not getting the same answer as the right answer, it's also a good idea to post your work so we can help you to see where you went wrong.

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

How do you quickly figure out that the square root of 1.15 is between 1.07 and 1.08?

Please advise.

my understanding of statement 2 is that it is insufficient because we do not have the variable n. therefore, the information to solve the equation is incomplete. can stacey, ron or someone please confirm this?

To GMAT TAKING SOON: A quick way to estimate sqrt(1.15) is to note that 1.15>1, so sqrt(1.15)>sqrt(1)=1. But 1.15^2 is too high, obviously greater than 1.15. The midpoint of 1.07 or 1.08 is close, so check those by squaring. 1.08^2 = 116.64 (too high). 1.07^2 = 114.49 (too low). Therefore r > 7.xxx.

To guest612: We would need n if the question concerned the value of I. However, this question is actually a Yes/No question concerning only the value of r: Is r > 8? Statement (2) is only insufficient because the computed range of r includes values both above and below 8.

_________________
Emily Sledge
Instructor
ManhattanGMAT

from statement b- if we consider r to be 8 from the question and substitute it in the second statement ( 1+r/100 )^2 > 1.15, then the value of the left side of the inequality is 1.1664 so even if 'r' is slightly less than 8, ex 7.9, then the value of LHS wud still be > 1.5 so B is not sufficient.

this will work. it's also an illustration of an important principle: if you want to check the effect of an INEQUALITY in DS, you should CHECK THE EXTREMES / BOUNDARY VALUES.
in other words, check for values near 8 percent, and for very small values. if they work out the same way, then "sufficient"; if not, then "insufficient".

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by the way, you don't have to do the arithmetic here. you can also realize that, if you compound by 8% twice, the result will have been increased by MORE than 16% (since the second compounding is performed on a value that's greater than the original). this realization is good enough (you don't have to calculate the exact value 1.1664), since all that matters is whether the overall gain is more than 15%.

I found plugging the value faster for (2).
1.08^2=1.1664. It is >1.15 BUT, what if the interest rate was just fractionally below 8%, we would perhaps get the value as 1.1660 (say), therefore insufficient.
Data in Statement 1 is of course sufficient to get a YES/NO answer.

that's a good insight.

Given that r is within a square term. Is it safe to assume from stmt 1 that r will have a unique value after solving the equation?

Thanks!

the term (1 + r/100) can't be negative in this problem, because "r" is the interest rate on an investment and is therefore a positive number.