vinni.k wrote:The population of a city rose at the rate of 10 percent every year, from the beginning of the year 1999 to the beginning of the year 2004. What was the population of the city at the start of the year 2000 ?

(1) The increase in the population of the city at the beginning of the year 2002 over that in the year 2001 was 25000

(2) The population of the city at the start of the year 2003 was 302,500.

Here's a slightly different approach.

Target question: What was the population at the start of the year 2000 ?
Given: the population increases 10% each year.
So, let X equal the population at the start of 1999
2000 population = (X)(1.1)
2001 population = (X)(1.1)(1.1) = (X)(1.1)^2
2002 population = (X)(1.1)(1.1)(1.1) = (X)(1.1)^3
2003 population = (X)(1.1)(1.1)(1.1)(1.1) = (X)(1.1)^4
2004 population = (X)(1.1)(1.1)(1.1)(1.1)(1.1) = (X)(1.1)^5

Rephrased target question: What is the value of (X)(1.1)?

IMPORTANT: To find the value of (X)(1.1), all we need is the value of X. So, a statement will be sufficient if we can use it to determine the value of X (which we'd then use to find the value of (X)(1.1). Given this, we can simplify the target question even more to get....

Rephrased target question: What is the value of X?

Statement 1: The increase in the population of the city at the beginning of the year 2002 over that in the year 2001 was 25000
In other words, (X)(1.1)^3 - (X)(1.1)^2 = 25000
Could we solve this equation for X?
Yes, we could (but we won't).
Since we can answer the rephrased target question with certainty, statement 1 is SUFFICIENT

Statement 2: The population of the city at the start of the year 2003 was 302,500.
In other words,
(X)(1.1)^4 = 302,500
Could we solve this equation for X?
Yes, we could (but we won't).
Since we can answer the rephrased target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent