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Question:On average, activated yeast cells divide once every 120 minutes; that is, each individual cell divides into two individual cells over that time span. Given that a certain yeast colony consisted of 310,000 cells two hours ago, approximately how many cells will be populating the colony six hours from now?
- 77,500
- 1,860,000
- 2,480,000
- 3,720,000
- 4,960,000
Approach Solution 1
Only one of the five options is correct.
If each yeast cell divides into two cells every 120 minutes (2 hours), and we want to determine the population of the colony after 4 intervals of 120 minutes (8 hours in total), we can calculate it as follows:
Number of cells after 4 intervals = Initial number of cells * (2^(time / division period))
Number of cells after 4 intervals = 310,000 * (2^(8 / 2))
Number of cells after 4 intervals = 310,000 * (2^4)
Number of cells after 4 intervals = 310,000 * 16
Number of cells after 4 intervals = 4,960,000
Therefore, the approximate number of cells populating the colony six hours from now is 4,960,000.
E is the correct answer.
Approach Solution 2
We can calculate the number of the colony at four 120-minute intervals (8 hours), assuming that each yeast cell splits into two cells every 120 minutes (2 hours).
The number of cells after 4 intervals is equal to the initial number of cells multiplied by (2(time / division period)).
After four intervals, the number of cells is equal to 310,000 * (8 / 2)
After four intervals, there will be 310,000 * (24) cells.
After four intervals, there will be 310,000 * 16 cells.
4,960,000 cells remain after four intervals.
The colony will therefore have 4,960,000 cells in it around six hours from now.
The right response is E.
Approach Solution 3
Assuming that each yeast cell divides into two cells every 120 minutes (2 hours), we can calculate the number of the colony at four 120-minute intervals (8 hours).
After four intervals, the number of cells is equal to the initial number of cells multiplied by (2(time / division interval)).
The number of cells after four intervals is equal to 310,000 * (8 / 2)
Four intervals later, there will be 310 000 * 24 cells.
Four intervals later, there will be 310,000,000 * 16 cells.
After four intervals, 4,960,000 cells remain.
In approximately six hours, the colony will therefore contain 4,960, 000 cells.
The correct answer is E.
“On average, activated yeast cells divide once every 120 minutes" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.
To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.
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