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Each cell of type X divides into a certain number of X-cells

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Each cell of type X divides into a certain number of X-cells [#permalink] New post 12 Jun 2011, 18:30
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Each cell of type X divides into a certain number of X-cells every hour. Each Type Y cell also divides into a constant number of Y-cells every hour, but not necessarily at the same rate as X. At a certain time, container A contained 10,000 X-cells and container B contained 10,000 Y-cells. After one hour, there were 30,000 more X-cells in container A than Y-cells in container B. After another hour, there were 330,000 more X-cells than Y-cells. What is the division rate per hour for the X-cells?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
[Reveal] Spoiler: OA

Last edited by smodak on 13 Jun 2011, 05:31, edited 1 time in total.
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Re: Cell Division [#permalink] New post 12 Jun 2011, 20:14
smodak wrote:
Each cell of type X divides into a certain number of X-cells every hour. Each Type Y cell also divides into a constant number of Y-cells every hour, but not necessarily at the same rate as X. At a certain time, container A contained 10,000 X-cells and container B contained 10,000 Y-cells. After one hour, there were 30,000 more X-cells in container A than Y-cells in container B. After another hour, there were 330,000 more X-cells than Y-cells. What is the division rate per hour for the X-cells?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

I will provide OA after some discussion.


X^2- (X-3)^2 =33
X^2-X^2+6X-9 = 33
6X=42
X= 7
Y =3
Its D

Last edited by sudhir18n on 12 Jun 2011, 23:10, edited 1 time in total.
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Re: Cell Division [#permalink] New post 12 Jun 2011, 23:04
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Division rate of X-cell = x cells/hour
Division rate of Y-cell = y cells/hour.

Starting quantity for X-cells in container A=10,000
Starting quantity for Y-cells in container B=10,000

After one hour, quantity of X-cells in container A=10,000x
After one hour, quantity of Y-cells in container B=10,000y
10,000x-10,000y=30,000
x-y=3 ----------(1)

Also, after another hour, quantity of X-cells in container A=(10,000x)x
after another hour, quantity of Y-cells in container B=(10,000y)y

(10,000x)x-(10,000y)y=330,000
x^2-y^2=33 -----------(2)

Substituting for y in (2)
x^2-(x-3)^2=33
x^2-x^2+6x+9=33
6x=42
x=7
Division rate of X-cell = 7 cells/hour

OA D.

Please let me know the OA.
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Re: Cell Division [#permalink] New post 12 Jun 2011, 23:11
at time t1 x = 10000, y = 10000, let rates be rx and ry each.

at time t2 x = 10000rx y = 10000 ry

at time t3 x = 10000rx * rx y = 10000ry * ry

now at t2 10000(rx-ry) = 30,000 rx-ry = 3

at t3 10000[ (rx+ry) * (rx-ry)] = 330,000

rx + ry = 11 rx - ry = 3

thus rx = 7 and ry = 4.

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Re: Cell Division [#permalink] New post 07 Apr 2013, 12:15
This questions is form GMAT Tutor. They advocate plugging in...which solution is better?
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Re: Cell Division [#permalink] New post 07 Apr 2013, 14:31
I plugged in numbers and I get C as the answer.
Now:
X = 10000
Y = 10000

After 1 hour, if constant growth rate of x = 6, then # x-cells in 1 hour = 10000 + (10000 * 6) = 70000
this is 30000 more than y cells after 1 hour, Therefore Y cells after 1 hour should be 40000
40000 Y cells = 10000 (original Y cells) + growth of 30000
that means Y growth multiple is 3 per hour

now after 1 more hour: X grows to 70000 + 70000*6 = 490000
Y is 330000 less than X after 2 hours so Y cells = 160000
160000 y cells = 40000 + 40000 * 3

hence IMO C should be the correct answer.
Re: Cell Division   [#permalink] 07 Apr 2013, 14:31
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