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Each cell of type X divides into a certain number of X-cells [#permalink]

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12 Jun 2011, 19:30

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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?

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 13 Jun 2011, 00:10, edited 1 time in total.

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

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

Each cell of Type X divides into a certain number of X-cells [#permalink]

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09 Jun 2014, 06:14

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?

Re: Each cell of Type X divides into a certain number of X-cells [#permalink]

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09 Jun 2014, 09:04

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goodyear2013 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

Let the division rate per hour for the X-cells be x and the division rate per hour for the Y-cells be y.

Initially: X-cells = 10,000 and y-cells = 10,000.

After 1 hour: X-cells = \(10,000x\) and y-cells = \(10,000y\). \(10,000x - 10,000y = 30,000\) --> \(x - y = 3\).

Re: Each cell of type X divides into a certain number of X-cells [#permalink]

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12 Jul 2014, 15:41

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Re: Each cell of type X divides into a certain number of X-cells [#permalink]

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24 Nov 2015, 19:25

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