parkhydel wrote:
Did the population of Town C increase by at least 100 percent from the year 2000 to the year 2010 ?
(1) The population of Town C in 2000 was 2/3 of the population in 2005.
(2) The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.
Target question: Did the population of Town C increase by at least 100 percent from the year 2000 to the year 2010 ?Aside: If a value increases by 100%, then that value is DOUBLED.
So, the target question is basically asking us
Did the population at least DOUBLE from year 2000 to 2010? Statement 1: The population of Town C in 2000 was 2/3 of the population in 2005. This tells us the population change from 2000 to
2005Since we need to know the population change from 2000 to
2010, statement 1 is NOT SUFFICIENT
Statement 2: The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005. Since statement 2 provides no information about the population change from 2000 to 2005, there's no way to answer the
target question with certainty
Statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Let X = the population in 2000
Let Y = the population in 2005
Let Z = the population in 2010
From statement 1, we can write: X = (2/3)Y
Multiply both sides of the equation by 3 to get: 3X = 2Y
Divide both sides by 2 to get: 3X/2 = Y
In other words,
Y = 1.5XStatement 2 tells us that the population increased by a greater NUMBER of people from 2005 to 2010 than it did from 2000 to 2005.
So let's first determine increase in the NUMBER of people from 2000 to 2005.
If
Y = 1.5X, we know the following:
X = the population in 2000
1.5X = the population in 2005
1.5X - X =
0.5XSo the population increased by
0.5X from 2000 to 2005
So, from 2005 to 2010, the population increased by AT LEAST
0.5X1.5X = the population in 2005
1.5X +
0.5X = 2.0X
So, the population in 2010 = was AT LEAST 2.0X
In other words, the population at least DOUBLED from 2000 to 2010
So, the answer to the target question is
YES, population of Town C DID increase by at least 100 percent from 2000 to 2010 Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent