Did the population of Town C increase by at least 100 percent from the

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

SMART NUMBERS APPROACH:


(1) Suppose population in Town C was 180 in 2005, \(\frac{180}{3}*2\)= 120 population in 2000.
Not sufficient, we have the range 2000-2005 not 2000-2010

(2) Clearly not sufficient, we don't have any value to answer the question.

(1) and (2)
For have at least 100% increase, the population in 2010 must be 240, +100% of 120.
From Statement 1: The increase from 2000 to 2005 was 180-120, thus + 60.
From Statement 2: The population of Town C increased by a greater number than range 2000-2005.
Thus increase > 60. Suppose it is 61, 180+61= 241> 240.

Sufficient.


Answer (C)

Did the population of Town C increase by at least 100 percent from the year 2000 to the year 2010 ?
Population in 2000 + Population in 2000 < Population in 2010
\(2*P_{2000} < P_{2010}\) ?

(1) The population of Town C in 2000 was 2/3 of the population in 2005.
\(P_{2000} = \frac{2}{3}*P_{2005}\)
Case I : \(P_{2010} = P_{2005} = \frac{3}{2}* P_{2000}\) NO
Case II: \(P_{2010} = 2*P_{2005} = 3*P_{2000}\) YES

INSUFFICIENT.

(2) The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.
Case I: \(P_{2000} = 100\), \(P_{2005} = 110\) and \(P_{2010} = 120\), So 20 > 10 But \(P_{2010} = 1.2*P_{2000}\) NO
Case II: \(P_{2000} = 100\), \(P_{2005} = 110\) and \(P_{2010} = 210\), So 110 > 10 But \(P_{2010} = 2.1*P_{2000}\) YES

INSUFFICIENT.

Together 1 and 2
\(P_{2005} - P_{2000} = (\frac{3}{2} - 1)*P_{2000} = \frac{1}{2}*P_{2000}\)
\(P_{2010} - P_{2005} > \frac{1}{2}*P_{2000}\)
\(P_{2010} > \frac{1}{2}*P_{2000} + P_{2005}\)
\(P_{2010} > \frac{1}{2}*P_{2000} + \frac{3}{2} * P_{2000}\)
\(P_{2010} > 2*P_{2000}\)

SUFFICIENT.

Answer C.
_________________

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.

Soln

We need to ans in Yes/No , whether increase in population from 2000 to 2010 was atleast 100% or not.
In other words- Did Population Double from year 2000 to year 2010??

St1 : The population of Town C in 2000 was 2/3 of the population in 2005.

- So if population in year 2000- Lets say was 6 ( Picking simple nos divisible by three) than population in 2005 would be 9
(since population increased by 2/3)

- But we don"t know if it was same increase or less from 2005 to 2010
- Hence St 1 insufficient

St 2 The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.

-No values given so we cannot say anything. Clearly insufficient

St 1+2 Together

In yr 2000- Population was 6
In yr 2005 - Population became 9 ( 2/3*9=6) ( as per st1 info)

Increase is by 3 which is 50% to population in yrs 2000

St 2 says that increase from 2005 to 2010 was more than increase from year 2000 to 2005. So if min increase was 4 .Population in 2010 would be 13 (9+4=13)

year 2000- population - 6 and year 2010- population 13 , which is clearly more than 100% increase or double

We have definite ans that increase was more than 100%

Hence Both statement together are sufficient.

Ans choice C

(1) Let, Population of 2005 = 120
So, the population of 2000 = 120*2/3 = 80

But NO information on population increment from 2000 to 2010 or 2005 to 2010 is given. INSUFFICIENT

(2) No increment rate or concept is given INSUFFICIENT.

USING BOTH THE OPTIONS:
2000 TO 2005 INCREMENT IS 40, 2005 TO 2010 IS GREATER THAN 40
SO THE PERCENTAGE INCREMENT WILL BE MORE THAN 80, WHICH ENSURES INCREMENT IS MORE THAN 100%
SUFFICIENT.

THE ANSWER IS C.
_________________

Let's,
The population in 2000 was 200 people

In 2005, the population in 2000 becomes 2/3 of the population in 2005.
So, if the population in 2000 was 200 people then the population in 2005 became 200*(3/2)= 300 people
Population increased = 300- 200 = 100 people

From 2005 to 2010, the population increased by a greater number than the increase in 2000 to 2005.
So, If from 2000 to 2005 the population increased by 100, then the population from 2005 to 2010 increased by more than 100. let's 110 people.

So, total increase (100+110) = 210

As 210 is more than 100% of the initial population of 200, So, taking both statements together we can say that the population increased by more than 100% from 2000 to 2010. So, [c] is the correct answer

Why does the variable approach from the math revolution not work here?

Solution:

A new og 2021 question

St (1):- The population of Town C in 2000 was 2/3 of the population in 2005.

There is no information about the population from 2000-2005. No information is provided about the population growth from 2000-2010.
(Insufficient)

St(2):- The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.

There is no information provided about the population growth either in percentage or absolute figures. (Insufficient)

Combining both ;

Let the population in 2005 =60

=> Population in 2000 = (2/3) *60 = 40

A 100% increase in 40 would mean a population of 80 in 2010

Increase from 2000-2005 = 60-40=20

Increase in number of people from 2005-2010 should be greater than 20 (St 2)

=>Minimum value of the pop then in 2010 would be 60+21=81 and 81>80(100% increase) (Sufficient)option (c)

Hope this helps
Devmitra Sen (GMAT Quant Expert)

Answer: Option C

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