At the beginning of 2010, 60% of the population of Town X li

ardz24 wrote:At the beginning of 2010, 60% of the population of Town X lived in the south and the rest lived in the north. During 2010, the population of Town X grew by 5.5%. If the population in the south grew by 4.5%, by how much did the population in the north grow?

A. 1%
B. 3.5%
C. 6.5%
D. 7%
E. 13.75%

Is there a strategic approach to this question? Can any experts help?

Imagine that 50% of the population lived in the south and 50% lived in the north. If that were true, each region would exert an equal weight in determining overall population growth. Put another way, if the overall growth were 5.5% and the south grew at 4.5%, the north would have grown at 6.5%, as 5.5 is smack dab in the middle of 4.5 and 6.5.

In this case, slightly less than half of the people live in the north, meaning that the population growth in the north would have be slightly more than 6.5% to compensate for its lesser impact on overall growth. The only answer that makes sense is D, 7%

ardz24 wrote:At the beginning of 2010, 60% of the population of Town X lived in the south and the rest lived in the north. During 2010, the population of Town X grew by 5.5%. If the population in the south grew by 4.5%, by how much did the population in the north grow?

A. 1%
B. 3.5%
C. 6.5%
D. 7%
E. 13.75%

Alternate approach:

Let the population in the south = 600 and the population in the north = 400, for a total of 1000 people.
Total growth for entire population of 1000 people = 5.5% of 1000 = 55.
Growth for the 600 people in the south = 4.5% of 600 = 27.
Growth for the 400 people in the north = (total growth) - (growth in the south) = 55-27 = 28.
Percentage growth in the north = (growth in the north)/(total in the north) * 100 = (28/400) * 100 = 7.

The correct answer is D.

ardz24 wrote:At the beginning of 2010, 60% of the population of Town X lived in the south and the rest lived in the north. During 2010, the population of Town X grew by 5.5%. If the population in the south grew by 4.5%, by how much did the population in the north grow?

A. 1%
B. 3.5%
C. 6.5%
D. 7%
E. 13.75%

We can let the total people in the town at the beginning of 2010 = n.

Thus, 0.6n = south and 0.4n = north.

We can determine the growth in the north by creating the following equation where x is the percent increase in the north:

1.045(0.6n) + (1 + x/100)(0.4n) = 1.055n

Divide both sides by n, we have:

0.627 + (1 + x/100)(0.4) = 1.055

(1 + x/100)(0.4) = 0.428

1+ x/100 = 1.07

x/100 = 0.07

x = 7

Alternate Solution:

Let’s assume the beginning population was 1000, so we know that 600 people lived in the south and 400 people lived in the north.

During 2010, the total population increased by 5.5%, so we have 1000 x 1.055 = 1055 citizens in the town at the end of 2010.

We know that the population in the south grew by 4.5%, so the population of the south was 600 x 1.045 = 627 at the end of 2010.

Thus, the population of the north at the end of 2010 had to be 1055 – 627 = 428. We use the formula for percent change: (New – Old)/Old x 100% , obtaining (428 – 400)/400 x 100% = 28/400 x 100% = 7%.

Answer: D