The chart shows the percentage of the total population of Country X

Question

https://gmatclub.com/forum/download/file.php?id=85830 The chart shows the percentage of the total population of Country X, measured at the end of each century, living in each of its four regions (Lowland, Highland, Coastal, and Desert). In each century, the population of every region increased compared with the prior century. From each drop-down menu, select the option that creates the most accurate statement based on the information given. The largest percentage increase in the total population from one century to the next occurred in the GRAPH_1_PLACEHOLDER Century, when the total population increased by GRAPH_2_PLACEHOLDER . GMAT-Club-Forum-x8kdoala.png

Bunuel · Accepted Answer

To determine the increase in total population from one century to the next, focus on the region whose share decreased the most. Since every region’s population increased, a decline in share means that the total must have risen enough to offset this growth.

•  17th to 18th Century:  Desert fell from 50% to 40%. Suppose the total population in the 17th Century was 100, so Desert had 50 people. In the 18th Century, Desert’s population was more than 50, which represented 40% of the new total. For 40% to exceed 50, the new total must have been more than 125, implying an increase of more than 25%.
•  18th to 19th Century:  Desert fell from 40% to 25%. If the 18th-Century total was 100, then Desert had 40 people. In the 19th Century, 25% had to exceed 40, so the new total had to be more than 160, which means an increase of more than 60%.
•  19th to 20th Century:  Desert fell from 25% to 10%. If the 19th-Century total was 100, then Desert had 25 people. In the 20th Century, 10% had to exceed 25, so the new total had to be more than 250. This means the population increased by more than 2.5 times, which corresponds to an increase of more than 150%.

Thus, the largest increase occurred in the  20th  Century, when the total population rose by  more than 150%  compared with the 19th Century.

I29-162

LucaBas34 · Answer

The intuition is as follows: Suppose there are 100 people living in the 19th century. For example, 25 of them lived in the desert. In the 20th century, this group increased by an amount  x . Although their total number grew, their percentage share fell to 10%. Thus, 25 + x now equals 10% of the total population. Therefore, the total population is 10 times (25 + x), which is greater than 250, representing an increase of more than 150%. 
 Hope this makes sense.

Dereno · Answer

The crux of this question lies in the statement : “   In each century, the population of every region increased compared with the prior century   “.

let’s take the 17th century population as 100. So, the lowland population: 10, Highland : 35, Coastal : 5, Desert: 50.

Look at the yellow bar ( DESERT) : In 17th century, it’s 50.

18th Century, let the total population be Y. 40%(Y) > 50. We get, Y > 125.

so, let’s take the population of 18th Century as 200.

Lowland : 30, Highland : 66, Coastal : 24 and Desert: 80.

Look at the yellow bar for 19th century, which is 25%. Let the population of 19th century be Z.

25% Z > 80. Then, Z > 320.

So, let the population of Z be 360.

Lowland : 65, Highland : 115, Coastal : 90 and Desert: 90.

Look at the yellow bar for 20th Century, which is 10%. Let the population of 20th century be P.

10% P > 90.

Thus, P has to be > 900.

Lets us take P =1000.

The individual values for 20th century are : Lowland (200), Highland (200), Coastal (450), Desert (100).

So, the POPULATION INCREASE is   highest from 19th century to 20th century  .

360 ————————> 1000 ( increase of 640)

640/360 = 177.77% (  MORE THAN 150%  ).

fugaquasi · Answer

Thank you so much for explaining this

findingmyself · Answer

fugaquasi   LucaBas34

The largest percentage increase in the total population from one century to the next occurred in the Century, when the total population increased by .

Largest population increase: Here we are bothered only about bars which are going up between one century to other, Why because, the decrease which are happening in another regions are compensated by the increase.

from 17th to 18th century: Net increase is 5+7=12 (Lowland 5% and Coastal 7%)
18th to 19th: Net increase is 16 (Lowland 3% Coastal 13%)
19th to 20th: Net increase is 22 (Lowland 2 and Coastal 20)
  Thus highest increase is in 20th centur  y

Now we can take the highest increase which happened, that is 19th century coastal from 25% to 45%
Let the overall population in 19th be x and 20th be y
We have 25% of X=45% of Y
Or X/4=9Y/20
X=9Y/5
 X is approximately 1.8Y, which is more than 160%

The chart shows the percentage of the total population of Country X

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