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MGMAT -D.S question - C.I.

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imhimanshu: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Sat Feb 28, 2009 7:01 am; Location: India; Thanked: 2 times

by imhimanshu » Mon Dec 05, 2011 3:19 am

Hi,
Can someone hep me with the below question -
Source -MGMAT

If a certain culture of bacteria increases by a constant factor of x every y minutes, how long will it take for the culture to increase to ten thousand times its original size.
1- x^(1/y)= 10
2 - In two minutes, the culture will increase to one hundred times its original size.

I coudn't manipulate choice 1. Pls help

OA to follow
Thanks

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Source: Beat The GMAT — Data Sufficiency | Mon Dec 05, 2011 3:19 am

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Mon Dec 05, 2011 4:10 am

Let A be the original size of the bacteria.
After y minutes, the size of the bacteria will be A*x
After 2y minutes, the size of the bacteria will be A*x*x
After 3y minutes, the size of the bacteria will be A*x*x*x
After 4y minutes, the size of the bacteria will be A*x*x*x*x
After n*y minutes, the size of the bacteria will be A*(x^n)

Given A*(x^n) = A*10000. Implies x^n = 10000. i.e x^n = 100^2 or x^n = 10^4.
If x^n = 10000^1 then x = 10000, n = 1 and time taken = y
If x^n = 100^2 then x = 100, n = 2 and time taken = 2y
If x^n = 10^4 then x = 10, n = 4 and time taken = 4y

1- x^(1/y)= 10

If x = 10000, then y = 4, n = 1 and time taken = y = 4
If x = 100, then y = 2, n = 2 and time taken = 2y = 4
If x = 10, then y = 1, n = 4 and time taken = 4y = 4
Sufficient !

2 - In two minutes, the culture will increase to one hundred times its original size.

After n*y minutes, the size of the bacteria will be A*(x^n).
here n*y = 2, and A*(x^n) = A*100. So x=10,n=2 and y=1 or x=100, n=1, and y=2

Solving for n,
If x =10, A*(x^n) = A*10000 => A*(10^n) = A*10^4 => n =4 and n*y = 4*1 =4
If x =100, A*(x^n) = A*10000 => A*(100^n) = A*100^2 => n =2 and n*y = 2*2=4
Sufficient!

IMO D
Correct me If I am wrong !

Anil Gandham
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Dec 05, 2011 5:02 am

imhimanshu wrote: If a certain culture of bacteria increases by a constant factor of x every y minutes, how long will it take for the culture to increase to ten thousand times its original size.
1- x^(1/y)= 10
2 - In two minutes, the culture will increase to one hundred times its original size.

Statement 1: x^(1/y) = 10.
[x^(1/y)]^y = 10^y.
x = 10^y.
Since 10,000 = 10â�´, x=10,000 when y=4.
Thus, it will take 4 minutes for the culture to increase to ten-thousand times its original amount.
SUFFICIENT.

Statement 2: In two minutes, the culture will increase to one-hundred times its original amount.
Thus, in 4 minutes, the culture will increase to 100*100 = 10,000 times its original amount.
SUFFICIENT.

The correct answer is D.

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imhimanshu: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Sat Feb 28, 2009 7:01 am; Location: India; Thanked: 2 times

by imhimanshu » Tue Dec 06, 2011 3:09 am

Thanks OA is D

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golu23: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Sat Jul 09, 2011 5:34 pmFollowed by: 1 member; Thanked: 1 times

by golu23 » Sat Dec 10, 2011 3:20 am

Hi Mitch could u please explain the first statement in an easy way possible i did understood it but only a little bit thnx

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Dec 10, 2011 3:58 am

golu23 wrote:Hi Mitch could u please explain the first statement in an easy way possible i did understood it but only a little bit thnx

The culture is to be multiplied by a factor of x=10,000.
y = the time needed.

Question rephrased: What is the value of y when x=10,000?

Statement 1: x^(1/y) = 10.

When one power is raised to another, we multiply the exponents.
To clear the fractional exponent, raise each side of the equation to the power of y:

[x^(1/y)]^y = 10^y.
x^(1/y * y) = 10^y
x = 10^y.

Plugging in x=10,000, we get:

10,000 = 10^y

Since 10,000 = 10â�´, y=4.
Thus, x=10,000 when y=4.
SUFFICIENT.

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