In a certain colony of cancerous cells

Question

In a certain colony of cancerous cells, each cell divides into two every hour. How many
will be produced from a single cell if the rate of division continues for 10 hours ?

I am confused with this question
should we use the population formulae F= I x^ (T/y)
or S = A(r^n -1) /( r-1)

1. With F= I x^ (T/y)
I get F = 1 * 2 ^10 = 1024

2. S = A(r^n -1) /( r-1)
1 2 4 8 .....
S = 1 (2 ^10 -1) /( 2-1) = 1024 -1 = 1023

Which approach is correct and why is the other formula wrong

neelgandham · Answer

Which approach is correct

- The first one , and

why is the other formula wrong

- If the question states that 'each cell gives birth to 2 cells every hour', then after the first hour we will be left with 3 cells (1 parent + 2 children - You can use the second formula in this case). But in this question, it is stated that each cells DIVIDES into two every hour, leaving us with just 2(2 children) after the first hour.

Number of cells a single cell divides into, in an hour (Hour 1) = 2
Number of cells these 2 cells divide into, in the next hour (Hour 2) = 2*2
Number of cells these 4 cells divide into, in the next hour (Hour 3)= 4*2 = 8 = 2^3
...
Number of cells these 2^9 cells divide into, in the 1th hour = 2* 2^9 = 2^10

So, 2^10 = 1024 is the correct answer.

p.s: I would suggest you to not use formulae while solving and to solve using simple mathematics.

Anil Gandham
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abcgmat · Answer

Thank you for explaining. I understood the difference But the answer to the question is 1023.

Ian Stewart · Answer

abcgmat wrote:Thank you for explaining. I understood the difference
But the answer to the question is 1023.

The total number of cells doubles every hour, so if k is a positive integer, then after k hours we certainly must have an even number of cells in total, no matter how many cells we begin with. But the wording of the question itself is a bit ambiguous; it asks "how many cells will be produced". You could take that to mean "how many cells will there be", in which case the answer is 1024, or you could take that to mean "how many more cells will you have after 10 hours than you had when you started" in which case the answer is 1024 - 1 = 1023. The wording of the question is open to two legitimate interpretations, so it's not a good question.

And I'd echo the advice given by neelgandham to avoid relying on formulas on GMAT questions, particularly if you are unsure of which formula to use. Most GMAT questions, at least at the higher level of the test, are immune to 'plug into a formula and solve' approaches.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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