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GMATPREP:Bank Account problem

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GMATPREP:Bank Account problem

by zaarathelab » Tue Oct 11, 2011 9:58 pm
If $1,000 is deposited in a certain bank account and remains in the account along with any accrued interest, the dollar amount of interest, I, earned by deposit in the first n years is given by 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 > 8%?
1) the deposit earns a total of $210 in interest in the first 2 years.
2) (1+r/100)^2 > 1.15

What is the quickest way to solve this?

[spoiler]Statement 1: Equation has only one unknown - hence SUFFICIENT
Statement 2: I first substituted 8 for r and found out that Interest(I) has to be > 176.4$. If i solve by substituting 1.15, I get Interest> 150$. I can be < or > than 176$. Hence INSUFFICIENT.

But this entire process took 4 minutes. [/spoiler]
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by 4GMAT_Mumbai » Tue Oct 11, 2011 10:08 pm
Hi zaarathelab,

I am afraid there is no drastically different way than the one that you have mentioned ...

Perhaps just a small variation would be to calculate (1.08)^2 = 1 + .0064 + .16 = 1.1664 and go from there ...

Thanks.
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by cans » Tue Oct 11, 2011 10:10 pm
is r>8 ??
b) when r=8, we will have 1.08^2 = 1.1664.
Thus insufficient. if r<8, we can have some value such that 1=r/100)^2 > 1.15 and < 1.16
a) we can find r.. sufficient
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by nandy1984 » Wed Oct 12, 2011 8:47 am
zaarathelab wrote:If $1,000 is deposited in a certain bank account and remains in the account along with any accrued interest, the dollar amount of interest, I, earned by deposit in the first n years is given by 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 > 8%?
1) the deposit earns a total of $210 in interest in the first 2 years.
2) (1+r/100)^2 > 1.15

What is the quickest way to solve this?

[spoiler]Statement 1: Equation has only one unknown - hence SUFFICIENT
Statement 2: I first substituted 8 for r and found out that Interest(I) has to be > 176.4$. If i solve by substituting 1.15, I get Interest> 150$. I can be < or > than 176$. Hence INSUFFICIENT.

But this entire process took 4 minutes. [/spoiler]
Hi zaarethelab,
In the DS problems as you might be knowing that we need not solve the problem. So you have done that in the first statement you know the values of I and n so you can say that its easy to tell that whether r>8?...so it could be less or more than 8. So you will have a definite answer for it...so its SUFFICIENT...
In the statement 2 lets see how our approach should be...they gave us the value
(1+r/100)^2 > 1.15...In these r>8 type of problems where we need to say either YES or NO...we need to find ways in which we can say YES to the answer and NO to the answer...If we are able to satisfy both then its INSUFFICIENT..if not then its SUFFICIENT...
Always start with opposite of what the question asks...mostly you will get the answer...
EX: since r>8 lets choose r=8
(1+0.08)^2=1.16 which is > 1.15...from this we can say that r not greater than 8 satisfies the inequality.
Now lets choose r=9 which is r>8
(1+0.09)^2 this will be definetly greater than 1.15...so r>8 also satisfies this inequality...
From this statement 2 we cannot definetly tell whether r is greater than 8 ... so insuficient...

Hopefully this has helped you...Its a big explanation but i tried my best to explain it properly...cans has said it smartly...thanks...
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by GMATGuruNY » Wed Oct 12, 2011 10:57 am
zaarathelab wrote:If $1,000 is deposited in a certain bank account and remains in the account along with any accrued interest, the dollar amount of interest, I, earned by deposit in the first n years is given by 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 > 8%?
1) the deposit earns a total of $210 in interest in the first 2 years.
2) (1+r/100)^2 > 1.15

What is the quickest way to solve this?
I used a similar approach but -- to save time -- estimated the result when r=8:

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