SPatel1992 wrote:
Hi!
I used a number to gauge:
Year 1= 100, Year 2= 120, Year 3= 140, Year 4=160, Year 5= 180 and Year 6= 200 (double of Year 1).
120/100= 1.2. I thought the answer was root 2.
Is this the correct method? How did you arrive at cube root 2?
As per question stem, a quantity increases in a manner such that the
ratio of its values in any two consecutive years is constant.
Let's check whether ratio of every two consecutive number in your solution is same or not
Year 1 = 100
Year 2 = 120
Year 3 = 140
Ratio of year 2 to 1 = (value in year 2) / (value in year 1)
= 120/100 = 1.2
Ration of year 3 to 2 = (value in year 3) / (value in year 2)
= 140/120 = 1.6667
Look, ratio of quantity increase in every two consecutive number is not same in the value taken by you; that is because you assumed that increase in the quantity is same every year. It is not anywhere mentioned in the question stem that quantity equally increases every year.
Here, the concept of compounding is used.
Here is the correct answer.
Suppose 1 becomes 2 after 6 years.
let x be the ratio by which 1 increases every year.
value of 1 after 6 years = 1 * (x)^6
so, 2 = 1 *(x)^6
Taking 6th root both side,
2^1/6 = x
So, x = 2^1/6
Value of 1 after 2 years = 1 * (X)^2
Value of 1 after 2 years = 1 * 2^1/6^2
Value of 1 after 2 years = 1 *2^1/3
Value of 1 after 2 years = 2^1/3 (which is third root of 2)
I hope this will be help to you in understanding.
Regards,
Balkrushna Vaghasia