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.
Answer is D
Please explain choice (1)
Thanks & Regards
Vinni
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The population of a city rose at the rate of 10 percent ever
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GMATGuruNY
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The population each year is 10% GREATER than that of the previous year: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.
Answer is D
Please explain choice (1)
Thanks & Regards
Vinni
2000 = (11/10) * 1999
2001 = (11/10) * 2000
2002 = (11/10) * 2001
2003 = (11/10) * 2002
2004 = (11/10) * 2003.
The result is that every year is in direct proportion to EVERY OTHER YEAR.
Thus, if the population in any particular year is known, the population in ALL OF THE OTHER YEARS -- including 2000 -- can be determined.
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.
From 2001 to 2002, the population grew by 25,000.
From 2001 to 2002, the population grew by 10%.
Thus, 25,000 is equal to 10% of the population in 2001:
25,000 = .1(2001)
2001 = 250,000.
SUFFICIENT.
Statement 2: The population of the city at the start of the year 2003 was 302,500.
SUFFICIENT.
The correct answer is D.
Last edited by GMATGuruNY on Sun Feb 03, 2013 9:04 am, edited 1 time in total.
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Here's a slightly different approach.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.
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
Brent Hanneson - Creator of GMATPrepNow.com
