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Each cell of type X divides into a certain number of Xcells [#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 Xcells every hour. Each Type Y cell also divides into a constant number of Ycells every hour, but not necessarily at the same rate as X. At a certain time, container A contained 10,000 Xcells and container B contained 10,000 Ycells. After one hour, there were 30,000 more Xcells in container A than Ycells in container B. After another hour, there were 330,000 more Xcells than Ycells. What is the division rate per hour for the Xcells? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8
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Last edited by smodak on 13 Jun 2011, 06:31, edited 1 time in total.



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Re: Cell Division [#permalink]
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12 Jun 2011, 21:14
smodak wrote: Each cell of type X divides into a certain number of Xcells every hour. Each Type Y cell also divides into a constant number of Ycells every hour, but not necessarily at the same rate as X. At a certain time, container A contained 10,000 Xcells and container B contained 10,000 Ycells. After one hour, there were 30,000 more Xcells in container A than Ycells in container B. After another hour, there were 330,000 more Xcells than Ycells. What is the division rate per hour for the Xcells?
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8
I will provide OA after some discussion. X^2 (X3)^2 =33 X^2X^2+6X9 = 33 6X=42 X= 7 Y =3 Its D
Last edited by sudhir18n on 13 Jun 2011, 00:10, edited 1 time in total.



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Re: Cell Division [#permalink]
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13 Jun 2011, 00:04
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Division rate of Xcell = x cells/hour Division rate of Ycell = y cells/hour. Starting quantity for Xcells in container A=10,000 Starting quantity for Ycells in container B=10,000 After one hour, quantity of Xcells in container A=10,000x After one hour, quantity of Ycells in container B=10,000y 10,000x10,000y=30,000 xy=3 (1) Also, after another hour, quantity of Xcells in container A=(10,000x)x after another hour, quantity of Ycells in container B=(10,000y)y (10,000x)x(10,000y)y=330,000 x^2y^2=33 (2) Substituting for y in (2) x^2(x3)^2=33 x^2x^2+6x+9=33 6x=42 x=7 Division rate of Xcell = 7 cells/hour OA D. Please let me know the OA.
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Re: Cell Division [#permalink]
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13 Jun 2011, 00:11
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(rxry) = 30,000 rxry = 3 at t3 10000[ (rx+ry) * (rxry)] = 330,000 rx + ry = 11 rx  ry = 3 thus rx = 7 and ry = 4. D.
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Re: Cell Division [#permalink]
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07 Apr 2013, 13:15
This questions is form GMAT Tutor. They advocate plugging in...which solution is better?



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Re: Cell Division [#permalink]
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07 Apr 2013, 15:31
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 # xcells 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.



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Each cell of Type X divides into a certain number of Xcells [#permalink]
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09 Jun 2014, 06:14
Each cell of Type X divides into a certain number of Xcells every hour. Each Type Y cell also divides into a constant number of Ycells every hour, but not necessarily at the same rate as X. At a certain time, container A contained 10,000 Xcells and container B contained 10,000 Ycells. After one hour, there were 30,000 more Xcells in container A than Ycells in container B. After another hour, there were 330,000 more Xcells than Ycells. What is the division rate per hour for the Xcells?
A. 4 B. 5 C. 6 D. 7 E. 8



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Re: Each cell of Type X divides into a certain number of Xcells [#permalink]
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09 Jun 2014, 09:04
goodyear2013 wrote: Each cell of Type X divides into a certain number of Xcells every hour. Each Type Y cell also divides into a constant number of Ycells every hour, but not necessarily at the same rate as X. At a certain time, container A contained 10,000 Xcells and container B contained 10,000 Ycells. After one hour, there were 30,000 more Xcells in container A than Ycells in container B. After another hour, there were 330,000 more Xcells than Ycells. What is the division rate per hour for the Xcells?
A. 4 B. 5 C. 6 D. 7 E. 8 Let the division rate per hour for the Xcells be x and the division rate per hour for the Ycells be y. Initially:Xcells = 10,000 and ycells = 10,000. After 1 hour:Xcells = \(10,000x\) and ycells = \(10,000y\). \(10,000x  10,000y = 30,000\) > \(x  y = 3\). After 2 hour:Xcells = 10,000x^2 and ycells = 10,000y^2. \(10,000x^2  10,000y^2 = 330,000\) > \((x  y)(x+y) = 33\). Since \(x  y = 3\), then \(3(x+y) = 33\) > \(x+y = 11\). Add this to \(x  y = 3\): \(2x=14\) > \(x=7\). Answer: D. Hope it's clear.
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