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10 May 2021, 23:00
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
59% (02:56) correct
41%
(03:02)
wrong
based on 113
sessions
History
Date
Time
Result
Not Attempted Yet
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
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
16 May 2021, 03:45
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Bunuel
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 = \(10,000y\).
\(10,000x - 10,000y = 30,000\) --> \(x - y = 3\).
After 2 hour:
X-cells = 10,000x^2 and y-cells = 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.
General Discussion
11 May 2021, 00:16
Kudos
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Let's solve by options
Answer D = 7: X = 10,000 ; Y = 10,000
- After 1 hour: X = 10,000 * 7 = 70,000 ; Y = 70,000 - 30,000 = 40,000 [Rate of Y becomes 4]
- After 1 more hour: X = 70,000 * 7 = 490,000 ; Y = 40,000 * 4 = 160,000
Difference: 490,000 - 160,000 = 330,000
Answer D
Answer D = 7: X = 10,000 ; Y = 10,000
- After 1 hour: X = 10,000 * 7 = 70,000 ; Y = 70,000 - 30,000 = 40,000 [Rate of Y becomes 4]
- After 1 more hour: X = 70,000 * 7 = 490,000 ; Y = 40,000 * 4 = 160,000
Difference: 490,000 - 160,000 = 330,000
Answer D
