In how many years, the amount x will grow to be 9 times the original v

Question

GMATBusters’ Quant Quiz Question -9

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John has deposited money in a bank to earn interest on his savings.
In how many years, the amount x will grow to be 9 times the original value?
1) The amount x is tripled in the first 12 years
2) The amount x accumulated after 18 years of the deposit is 4x

ashwini2k6jha · Answer

Answer E
state 1:not sufficient
given x becomes 3 x in first 12 years
we don't know multiplying factor as it is not given.factor may be constant or variable
Hence we can not calculate time for to be 9 x
state :2 not sufficient
given 3 x in 18 years 
simillar to previous case ,we are not given factor constant or variable
state 1+2 not sufficient

uc26 · Answer

We need to find the interval in which the amount increases by x.
1) Not enough information to find an interval. Not sufficient.
2) Not enough information to find an interval. Not sufficient.
 
1&2) Enough to find an interval. The amount increases by x every 6 years. Sufficient.

Answer: C

Archit3110 · Answer

original value X ; in how many years it becomes 9X
#1
The amount x is tripled in the first 12 years
tripled in 12 years ; 
so for every 4 years it gains a multiple so it would become 9 times in 36 years ; considering that its a linear growth or it may not be 
so insufficient
#2
The amount x accumulated after 18 years of the deposit is 4x
every 4.5 years its growing so in 4.5*9 ; 40.5 years it will take considering that its a linear growth or it may not be 
so insufficient

from1 &2 we can say that over period of 12th to 18th years i.e 6 years 
which means in every 6 years there is an increase in unit 
so it would take 48 years to become 9 times original value
OPTION C

In how many years, the amount x will grow to be 9 times the original value?
1) The amount x is tripled in the first 12 years
2) The amount x accumulated after 18 years of the deposit is 4x

Kinshook · Answer

Asked: In how many years, the amount x will grow to be 9 times the original value?

1) The amount x is tripled in the first 12 years
Since it is not mentioned whether the amount is growing at a constant compounded rate.
NOT SUFFICIENT

2) The amount x accumulated after 18 years of the deposit is 4x 
Since it is not mentioned whether the amount is growing at a constant compounded rate.
NOT SUFFICIENT

(1) + (2) 
1) The amount x is tripled in the first 12 years
2) The amount x accumulated after 18 years of the deposit is 4x 
Since it is not mentioned whether the amount is growing at a constant compounded rate.
NOT SUFFICIENT

IMO E

MayankSingh · Answer

IMO C

In how many years, the amount x will grow to be 9 times the original value?

1) The amount x is tripled in the first 12 years

If under CI,
 X  ...... 12 Yr........  3X  .......... 24 Yr ..............  9X 
So, Years =24

But if Under SI, 
SI=2x
2x= x r 12/100
r = 100/6
So, 8x = x 100/6*100 x T
T= 48
So T not fixed.

Not sufficient.

2) The amount x accumulated after 18 years of the deposit is 4x
Similar to 1, Under CI or under SI will give different values of T

Not Sufficient

Together,   
If under CI
 X  ...... 12 Yr........  3X  .......... 24 Yr ..............  9X ............36 Yr............. 27X 
 X  ...... 18 Yr........  4X  .......... 36 Yr ..............  16X 
From above we can see that, if T=36 Yr, St 1 gives Amount = 27X but St 2 = 16X
So Interest is not CI

So,Under SI.
Both 1 & 2 give, r=100/6
T=48 Yr
Sufficient...

yashikaaggarwal · Answer

IMO C

Statement 1 says the amount triples in 12 years.
But at what rate it reached triple amount in 12 years? (Not sufficient)

Statement 2: says the amount four times itself in 18 years. But at what rate it reached 4 times value? (Not sufficient)

Statement 1&2 says: 3x in 12 years
4x in 18 years.
100% in 6 years
Therefore, it will reach 9times in 48 years.

Posted from my mobile device

dexter12345 · Answer

48 years.

Took 12 years to become 3x (2x growth)
Took 18 years to become 4x (3x growth)

So it's a simple interest problem, where every 6 years, it grows by 1x. So for 9x, it takes 48 years.

tyson1990 · Answer

lets say, interest per year = r
9X = X . (1+r)^y ... (eq-1)
find y = ?

From ST(1), 3X = X . (1+r)^12
3 = (1+r)^12
9 = 3^2 = (1+r)^24

Hence, y = 24

ST(1) is sufficient.

From ST(1), 4X = X . (1+r)^18
(1+r)^18 = 4
18 . log(1+r) = log(4)
log(1+r) = log(4)/18

Now, from eq-1, we can find 
y . log(1+r) = log(9)
y . log(4)/18 = log(9)
y = 18 . log(9) / log(4)
y ~ 28.xxx

ST(2) is sufficient .

Kinshook · Answer

Hi  GMATBusters 
Future events may not depend on the past. 
Future is uncertain, in stock market also even if the above 2 statements are TRUE regarding a stock, it may still go down to even zero (0)
Unless it is explicitly mentioned that amount grows according to some rule, IMO E
Please correct OA.

Kinshook · Answer

Bunuel 
Please check and resolve!

GMATBusters · Answer

The question stem revised to add clarity.

Thanks

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In how many years, the amount x will grow to be 9 times the original v

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