BTGModeratorVI wrote: ↑

Thu Nov 05, 2020 7:54 am

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.

Answer: C
Source: official guide

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 2005
Since 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 = 1.5X

Statement 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 = 0.5X
So the population increased by 0.5X from 2000 to 2005
So, from 2005 to 2010, the population increased by AT LEAST 0.5X

1.5X = 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