The annual birth and death rate in a country per 1000 are 39.4 and 19.

Question

The annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years in which the population would be doubled assuming there is no emigration or immigration is

A. 20
B. 25
C. 30
D. 35
E. 40

ankitranjan · Answer

Suppose the population of the country in current year is 1000.
 So annual increase is 1000 + 39.4 - 19.4=1020
Hence every year there is an increase of 2%.

2000=1000(1+(2/100))^n

n=35 Answer is D. (But Calculation is somewhat tedious.) Anything simple than this?

Consider KUDOS if its helpful.

metallicafan · Answer

Yes, I also solved it in that way. The problem is that you cannot use a scientific calculator during the exam LOL.
I think we need the help of the moderators!

kcr2210 · Answer

An easier method is the Rule of 70 which is a simple way to calculate the approximate number of years it takes for the level of a variable growing at a constant rate to double. This rule states that the approximate number of years n for a variable growing at the constant growth rate of R percent, to double is

n = 70/R

Since B-D = 39.4-19.4 = 20 normalized to 1000 = 2%

The n = 70/2 = 35

n = 70/R

Since B-D = 39.4-19.4 = 20 normalized to 1000 = 2%

The n = 70/2 = 35

guijob · Answer

wow! I have never heard about this, interesting... 
Do you have any support to prove this approach will always show me the right answer?

Thank you for your reply.

KarishmaB · Answer

You can use the n = 70/r rule whenever you want the amount to double in an annual compounded interest rate scenario but GMAT doesn't expect you to know this formula so the calculations will either be simpler or the formula will be given in the question.

ssriva2 · Answer

Can anyone guide me how to solve this manually.I don't have any clue.

2000=1000(1+(2/100))^n

KarishmaB · Answer

You cannot solve it manually. You need a calculator to do it. 
Though, when the amount is twice the principal, we have a simple formula (which will be given in the question if this question comes in GMAT) 
The principal doubles in 70/r years. 
Since the rate of interest is 2% here, and the principal doubles from 1000 to 2000, the number of years it will take is 70/2 = 35 years.

ssriva2 · Answer

You cannot solve it manually. You need a calculator to do it. 
Though, when the amount is twice the principal, we have a simple formula (which will be given in the question if this question comes in GMAT) 
The principal doubles in 70/r years. 
Since the rate of interest is 2% here, and the principal doubles from 1000 to 2000, the number of years it will take is 70/2 = 35 years.

Thanks a lot Karishma.I usually get struck on this last part in these kind of questions.

faltan · Answer

a question of 800 band

)

baris800 · Answer

I have found the interest formula but clearly it can not be solved without a calculator. Then, I devised another solution.

Another approach to solve this:

At first, the population increases by 20.
At last, the population increases by just short of 40. (Increase would be 40 if population were 2000 exactly.)

Therefore, the average amount of increase per year is just short of 30. If it were 30, it would take 1000/30=33.3 years to double. But we know it must be slightly more than that because average is lower than 30.

Hence, it must be bigger than 33.3 but only slightly bigger. Answer is 35. (D)

Regor60 · Answer

Bad question. Why is it still here ?

The annual birth and death rate in a country per 1000 are 39.4 and 19.

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