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If John deposited 1000$ in a certain bank account, where the interest

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New post 29 Sep 2018, 10:37
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Weekly Quant Quiz Question -8



If John deposited 1000$ in a certain bank account, where the interest earned in a year is given by Interest = Principal deposited \([(1+\frac{x}{100})^n -1]\), where x is annual interest paid by the bank. Is the annual interest greater than 7%?
a) The interest earned in a two-year period is 210$.
b) \((1+\frac{x}{100})^n >1.14\)

Only the TEXT Solution is Allowed


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Re: If John deposited 1000$ in a certain bank account, where the interest  [#permalink]

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New post 29 Sep 2018, 22:12
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Official Solution:


Statement1: The interest earned in a two-year period is 210$.
Since we don't know whether the interest earned is in first 2-year period or 10-12 year period or so, nothing can be said about the rate of interest.
NOT SUFFICIENT
Statement 2: \((1+\frac{x}{100})^n >1.14\)
Since value of n is not given, we can not say anything about rate of interest.
NOT SUFFICIENT
Even after combining statement 1 & 2, we can not say anything about rate of interest.
NOT SUFFICIENT
Answer E

gmatbusters wrote:

Weekly Quant Quiz Question -8



If John deposited 1000$ in a certain bank account, where the interest earned in a year is given by Interest = Principal deposited \([(1+\frac{x}{100})^n -1]\), where x is annual interest paid by the bank. Is the annual interest greater than 7%?
a) The interest earned in a two-year period is 210$.
b) \((1+\frac{x}{100})^n >1.14\)

Only the TEXT Solution is Allowed


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Re: If John deposited 1000$ in a certain bank account, where the interest  [#permalink]

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New post 29 Sep 2018, 10:44
Answer is A

As per first statement for a period of 2 year interest is 210....With 7% interest Interest will be arounf 140...hence 210 is much higher hence A is SUFFICIENT

As per second statement b) (1+/100)^n>1.14 we have no clue about number of years or interst rate...if it is 1 year then yes if it is 2 years or more than no...Hence INSUFFICIENT
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New post 29 Sep 2018, 10:46
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Solving for equation 1 we have rate as 10, statement 1 is therefore sufficient, statement isn't sufficient since values of x and n can be varied to satisfy tje equation

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Re: If John deposited 1000$ in a certain bank account, where the interest  [#permalink]

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New post 29 Sep 2018, 10:47
1
St a)

210 = 1000*((1+x/100)^2 -1)

On simplifying a bit... divide by 1000 and take 1 to LHS...
1.21 = (1+x/100)^2
1.21 = (1+x%)^2
1.21 = 1 + 2x + x^2 ( we can ignore x^2 as it will be a negligible amount)
1.21 = 1 + 2x

x = 10.5%

St a) is sufficient.

St b) From above simplification -
1.14 < 1+2x
x > 7%

Hence St b) is also sufficient.

hence Option (D) is correct.

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New post 29 Sep 2018, 10:48
E.

1) NS ....... no info about n.... the time frame of compounding
2) NS ....... no info about n.... the time frame of compounding
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Re: If John deposited 1000$ in a certain bank account, where the interest  [#permalink]

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New post Updated on: 29 Sep 2018, 21:50
Statement I:

P[\((1+x/100)^2−1]\)= 210

P = 1000

x = 10. Hence, Sufficeient.


Statement II

[\((1+x/100)^n]\) > 1.14
Here, X can be 7 or greater than 7 for n>= 2.
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Originally posted by rahul16singh28 on 29 Sep 2018, 10:48.
Last edited by rahul16singh28 on 29 Sep 2018, 21:50, edited 1 time in total.
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Re: If John deposited 1000$ in a certain bank account, where the interest  [#permalink]

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New post 29 Sep 2018, 10:51
from 1 st equation 210/1000=[(1+x%)^2-1]

solving we get
x^2+200x-2100=0

Solving we get,
x=10,-210
answer is 10 therefore sufficient

solving for second prompt given
(1+x/100)^n>1.14
solving we get nx/100=14/100
nx=14 therefore n=2,7 x=7,2 not sufficient

Answer=A
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Re: If John deposited 1000$ in a certain bank account, where the interest  [#permalink]

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New post 29 Sep 2018, 12:47
Ans A

Principal = 1000

210 = 1000((1+(x/100)raised to power n) -1)

Here n=2

Thus, upon solving,

We get,

121 = 100(1 + (x/100))raises to power 2

Taking square root on both sides, we get

11 = 10+ (x/10)

Thus, x =10.

Solving for n =1, we get x >14, so yes

For n =2, 1+(x/100) > 1.5

X>50 so yes.

So ans is D , both are sufficient

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Re: If John deposited 1000$ in a certain bank account, where the interest   [#permalink] 29 Sep 2018, 12:47
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