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01 Nov 2010, 17:32
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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 $$I=1,000((1+\frac{r}{100})^n-1)$$, 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) $$(1 + \frac{r}{100})^2 > 1.15$$

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15 Mar 2013, 16:47
5
I think the gmat is always about insight and not about arithemetic
.
Question: Is r>8%? If r can be 8 percent or greater, the statement will be insufficient.

Stmt 2) Overall interest earned over two years, is greater than 15% (If you read this far down, you know what I am talking about)
Lets say the interest was 8%, then overall compound interest earned over two years will be greater than 16% and so greater than 15%
It goes without saying that if the interest rate was greater than 8%, then the amount of interest earned over two years, will still be greater than 15%.

It took me 1:30 seconds to see this, and another 40 seconds to type this entire post because I was not satisfied with the explanations given
.No messy calculations or nail biting necessary.
##### General Discussion
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Re: If $1,000 is deposited in a certain bank account and remains in the [#permalink] ### Show Tags 01 Nov 2010, 20:07 13 16 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?

Given: $$I=1,000((1+\frac{r}{100})^n-1)$$. Question: is $$r>8$$.

(1) The deposit earns a total of $210 in interest in the first two years --> $$I=210$$ and $$n=2$$ --> $$210=1,000((1+\frac{r}{100})^2-1)$$ --> note that we are left with only one unknown in this equation, $$r$$, and we'll be able to solve for it and say whether it's more than 8, so even withput actual solving we can say that this statement is sufficient. (2) (1 + r/100 )^2 > 1.15 --> if $$r=8$$ then $$(1+\frac{r}{100})^2=(1+\frac{8}{100})^2=1.08^2\approx{1.16}>1.15$$ so, if $$r$$ is slightly less than 8 (for example 7.99999), $$(1+\frac{r}{100})^2$$ will still be more than 1.15. So, this statement is not sufficient to say whether $$r>8$$. Answer: A. _________________ Intern Joined: 18 Aug 2010 Posts: 10 Re: If$1,000 is deposited in a certain bank account and remains in the  [#permalink]

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01 Nov 2010, 20:16
ah... for S2, I approached it from the other angle and had to take the square root of 1.15. I got stuck there and time was running out, so I took a guess. It's much easier to multiply 1.08 by 1.08 than to take the square root of 1.15.

Thanks!
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Re: If $1,000 is deposited in a certain bank account and remains in the [#permalink] ### Show Tags 25 Dec 2012, 20:42 Bunuel wrote: 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?

Given: $$I=1,000((1+\frac{r}{100})^n-1)$$. Question: is $$r>8$$.

(1) The deposit earns a total of $210 in interest in the first two years --> $$I=210$$ and $$n=2$$ --> $$210=1,000((1+\frac{r}{100})^2-1)$$ --> note that we are left with only one unknown in this equation, $$r$$, and we'll be able to solve for it and say whether it's more than 8, so even withput actual solving we can say that this statement is sufficient. (2) (1 + r/100 )^2 > 1.15 --> if $$r=8$$ then $$(1+\frac{r}{100})^2=(1+\frac{8}{100})^2=1.08^2\approx{1.16}>1.15$$ so, if $$r$$ is slightly less than 8 (for example 7.99999), $$(1+\frac{r}{100})^2$$ will still be more than 1.15. So, this statement is not sufficient to say whether $$r>8$$. Answer: A. Hello Bunuel, your explanation for second DS choice suggests that, if we have only 1 variable in the equation, then we need not solve it. However, I have observed few of the GMAT problems that have similar quadratic equations (with second degree) solve to two different positive roots, hence the DS choice could not be true. I believe it would be safe to solve the equation until you know if its only going to give you "one" root. e.g. $$ax^2+bx-c=0$$, this equation will have one positive and one negative root. As rate in this case is supposed to be positive, hence only 1 root. However, if the equation resolves to $$ax^2-bx+c=0$$ then it can have two positive roots (one of which may be less than 8 and other more than 8), hence the choice may not be true. Only if both positive roots are more than 8, then the choice can be taken as true. Please advice. _________________ Thanks, Prashant Ponde Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7 Reading Comprehension notes: Click here VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here Looking to finance your tuition: Click here VP Status: Been a long time guys... Joined: 03 Feb 2011 Posts: 1263 Location: United States (NY) Concentration: Finance, Marketing GPA: 3.75 Re: If$1,000 is deposited in a certain bank account and remains in the  [#permalink]

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02 Jan 2013, 21:32
2
1
kiyo0610 wrote:
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 >1.15

statement 1) I=$210, n=2 Putting this in the equation given in the question, we will be able to find the value of r and thereby be able to answer the question. Suffiicient. Statement 2) Using Binomial theorem, we can infer $$(1+r/100)^2 > 1.15$$ as $$(1+2r/100) > 1.15$$. On solving this relation we will get, r>7.5. But since its not given that r is an integer then r can be 7.51, 7.6,9, 11 etc. Hence insufficient. +1A _________________ GMAT Club Legend Joined: 16 Oct 2010 Posts: 8135 Location: Pune, India Re: If$1,000 is deposited in a certain bank account and remains in the  [#permalink]

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14 Mar 2013, 21:16
3
1
Responding to a pm:
Question: (1 + .08)^2 = ?

$$1.08 = \frac{108}{100}$$ (it's trickier to deal with decimal so remove it)

$$(\frac{108}{100})^2 = \frac{108^2}{10000}$$

We know how to get the square of 108
$$108^2 = 11664$$ (discussed in the post above)

So, $$(1 + .08)^2 = 11664/10000 = 1.1664$$

Or you can use (a + b)^2 = a^2 + b^2 + 2ab (the shortcut is anyway based on this formula only)

(1 + .08)^2 = 1 + .0064 + 2*1*.08 = 1.1664
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Re: If $1,000 is deposited in a certain bank account and remains in the [#permalink] ### Show Tags 15 Mar 2013, 00:40 Marcab wrote: kiyo0610 wrote: 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 $210 in interest in the first two years. (2) (1+r/100)^2 >1.15 The total interest is given as I=1,000[(1+r/100)^n - 1]. From F.S 1 we have that I = 210. Thus, we have a quadratic equation and we know that it can be solved leading to a fixed value for r. Sufficient.Also, one can notice that an interest of 210$ is obtained when r=10% and this is greater than 8%. Sufficient.

From F.S 2, we know that n=2. And the Interest earned would be greater than 150.Thus, I=1,000[(1+r/100)^2 - 1] = $$1000[r/100*(2+\frac{r}{100})]$$. We know for r=8% we have this equal to 2.08*80 = 166.4 which is anyways greater than 150. Now, for r=7%, the expression equals 2.07*70 = 144.9. Thus, for a value between 7 and 8 , this value will change and become more than 150. Thus we wouldn't know for sure if r>8 or not. Insufficient.

A.
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19 Mar 2013, 11:37
hi all , why not D?
From first statement, one can answer that interest rate is greater than 8%
From second second statement, one can answer that interest rate is less than 8%

So, either statement can be used to answer the question. Am I missing any thing? Please reply.
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29 Mar 2013, 08:54
Bunuel wrote:
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? Given: $$I=1,000((1+\frac{r}{100})^n-1)$$. Question: is $$r>8$$. (1) The deposit earns a total of$210 in interest in the first two years --> $$I=210$$ and $$n=2$$ --> $$210=1,000((1+\frac{r}{100})^2-1)$$ --> note that we are left with only one unknown in this equation, $$r$$, and we'll be able to solve for it and say whether it's more than 8, so even withput actual solving we can say that this statement is sufficient.

(2) (1 + r/100 )^2 > 1.15 --> if $$r=8$$ then $$(1+\frac{r}{100})^2=(1+\frac{8}{100})^2=1.08^2\approx{1.16}>1.15$$ so, if $$r$$ is slightly less than 8 (for example 7.99999), $$(1+\frac{r}{100})^2$$ will still be more than 1.15. So, this statement is not sufficient to say whether $$r>8$$.

Bunuel,

As this is a quadratic equation , how did you concluded that we will get one value after solving this equation?
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Re: If $1,000 is deposited in a certain bank account and remains in the [#permalink] ### Show Tags 17 Jul 2013, 11:15 greatps24 wrote: Bunuel wrote: 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?

Given: $$I=1,000((1+\frac{r}{100})^n-1)$$. Question: is $$r>8$$.

(1) The deposit earns a total of $210 in interest in the first two years --> $$I=210$$ and $$n=2$$ --> $$210=1,000((1+\frac{r}{100})^2-1)$$ --> note that we are left with only one unknown in this equation, $$r$$, and we'll be able to solve for it and say whether it's more than 8, so even withput actual solving we can say that this statement is sufficient. Bunuel, As this is a quadratic equation , how did you concluded that we will get one value after solving this equation? Same question for Bunuel or any of the other experts here. My calculations: 1) $$210 = 1000 [(1+\frac{r}{100})^2-1)$$ 2) $$210 = 1000 [1+\frac{2r}{100}+\frac{r^2}{10000}-1]$$ 3) $$210=1000(\frac{200r+r^2}{10,000})$$ 4) $$210=\frac{200r+r^2}{10}$$ 5) $$2100=r(200+r)$$ How do you solve for the variable r at this point? Any further explanation would help. ~ Im2bz2p345 GMAT Club Legend Joined: 16 Oct 2010 Posts: 8135 Location: Pune, India Re: If$1,000 is deposited in a certain bank account and remains in the  [#permalink]

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17 Jul 2013, 21:05
2
2
Im2bz2p345 wrote:
greatps24 wrote:
Bunuel wrote:
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? Given: $$I=1,000((1+\frac{r}{100})^n-1)$$. Question: is $$r>8$$. (1) The deposit earns a total of$210 in interest in the first two years --> $$I=210$$ and $$n=2$$ --> $$210=1,000((1+\frac{r}{100})^2-1)$$ --> note that we are left with only one unknown in this equation, $$r$$, and we'll be able to solve for it and say whether it's more than 8, so even withput actual solving we can say that this statement is sufficient.

Bunuel,

As this is a quadratic equation , how did you concluded that we will get one value after solving this equation?

Same question for Bunuel or any of the other experts here.

My calculations:

1) $$210 = 1000 [(1+\frac{r}{100})^2-1)$$

2) $$210 = 1000 [1+\frac{2r}{100}+\frac{r^2}{10000}-1]$$

3) $$210=1000(\frac{200r+r^2}{10,000})$$

4) $$210=\frac{200r+r^2}{10}$$

5) $$2100=r(200+r)$$

How do you solve for the variable r at this point?

Any further explanation would help.

~ Im2bz2p345

Solving this quadratic is a little time consuming though we will see how to do in a minute. But you don't really need to solve it to figure out that you will have only one solution.

$$2100=r(200+r)$$
$$r^2 + 200r - 2100 = 0$$

In a quadratic, $$ax^2 + bx + c = 0$$, sum of the roots = -b/a and product of the roots = c/a
Notice that the product of the roots (-2100) is negative. This means one root is positive and the other is negative. So we will have only one acceptable solution (the positive one)

Now, if you would like to solve it:
$$r^2 + 200r - 2100 = 0$$

2100 = 2*2*5*5*3*7
Now you need to split 2100 into two factors such that one is a little larger than 200 and the other is a small factor e.g. 5 or 7 or 10 etc. Once you think this way, you easily get 210 and 10

$$r^2 + 210r - 10r - 2100 = 0$$
(r + 210)(r - 10) = 0
r = -210 or 10
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17 Jul 2013, 23:49
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Im2bz2p345 wrote:
greatps24 wrote:
Bunuel wrote:
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? Given: $$I=1,000((1+\frac{r}{100})^n-1)$$. Question: is $$r>8$$. (1) The deposit earns a total of$210 in interest in the first two years --> $$I=210$$ and $$n=2$$ --> $$210=1,000((1+\frac{r}{100})^2-1)$$ --> note that we are left with only one unknown in this equation, $$r$$, and we'll be able to solve for it and say whether it's more than 8, so even withput actual solving we can say that this statement is sufficient.

Bunuel,

As this is a quadratic equation , how did you concluded that we will get one value after solving this equation?

Same question for Bunuel or any of the other experts here.

My calculations:

1) $$210 = 1000 [(1+\frac{r}{100})^2-1)$$

2) $$210 = 1000 [1+\frac{2r}{100}+\frac{r^2}{10000}-1]$$

3) $$210=1000(\frac{200r+r^2}{10,000})$$

4) $$210=\frac{200r+r^2}{10}$$

5) $$2100=r(200+r)$$

How do you solve for the variable r at this point?

Any further explanation would help.

~ Im2bz2p345

Actually you don't need to solve this way:

$$1,000((1+\frac{r}{100})^2-1)=210$$

$$(1+\frac{r}{100})^2-1=\frac{210}{1,000}$$

$$(1+\frac{r}{100})^2=\frac{21}{100}+1$$

$$(1+\frac{r}{100})^2=\frac{121}{100}$$

$$1+\frac{r}{100}=\frac{11}{10}$$ ($$1+\frac{r}{100}$$ cannot equal to $$-\frac{11}{10}$$ because it would men that r is negative.)

$$1+\frac{r}{100}=\frac{11}{10}$$

$$\frac{r}{100}=\frac{1}{10}$$

$$r=10$$
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01 Nov 2015, 00:26
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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 > 1.15

There are 3 variables (r,I,n) and 1 equation (I=1,000((1+r/100)^n-1) in the original condition, 2 equations from the 2 conditions; there is high chance (C) will be our answer.
In condition 1, there are 2 equations, and if the interest is $210, the interest rate is either greater (yes) or smaller (no) than 8%, therefore sufficient. In condition 2, (1.08)^2=1.1664, the interest rate is not greater than 8%, so this is insufficient. Therefore the answer becomes (A). For cases where we need 2 more equation, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: If $1,000 is deposited in a certain bank account and remains in the [#permalink] ### Show Tags 20 Jan 2016, 13:36 butterfly wrote: 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 > 1.15 No need for complex calculations here. (1) Interest=210 r=10% (if you have done several compound interest problems this number is very frequent, so I could see this within 10 seconds because of my previous experience). Sufficient (2) This statment tells us that r was slightly more than 7,5% --> see 1,15 on the other side, so r can be <>8% . Not Sufficient Amswer A _________________ When you’re up, your friends know who you are. When you’re down, you know who your friends are. Share some Kudos, if my posts help you. Thank you ! 800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660 Re: If$1,000 is deposited in a certain bank account and remains in the &nbs [#permalink] 20 Jan 2016, 13:36

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