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. Country X’s total population had to increase by the greatest percentage from the previous century to the GRAPH_1_PLACEHOLDER Century, when the total population had to increase by GRAPH_2_PLACEHOLDER . GMAT-Club-Forum-x8kdoala.png

Bunuel · Accepted Answer

Official Solution:

To determine how much the total population  had to  increase from one century to the next, focus on the region whose share decreased the most. Since every region’s actual population increased, the smaller percentage in the next century still had to represent more people than the larger percentage in the previous century. For example, if a region’s share fell from 50% to 40%, then 40% of the new total had to be greater than 50% of the previous total.

•  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 and represented 40% of the new total. For 40% of the new total 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% of the new total 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% of the new total had to exceed 25, so the new total had to be more than 250. Thus, the new total had to be more than 2.5 times the previous total, which corresponds to an increase of more than 150%.

Thus, Country X’s total population had to increase by the greatest percentage from the 19th Century to the  20th  Century, when it had to increase by  more than 150% .

Correct answer:

Dropdown 1:  "20th"

Dropdown 2:  "more than 150%"

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%

WildSnow · Answer

Bunuel  I really liked the question. I have two questions. First, why are we calculating on the basis of Desert percentages? 
Second, 
 •  17th to 18th Century:  an increase of more than 25%.  
 •  18th to 19th Century:  increase of more than 60%. 
 •  19th to 20th Century:  an increase of more than 150%.

so how come the largest increase occurred in the  20th  Century? It is possible that the largest increase occurred in 17th to 18th?

egmat · Answer

Hi WildSnow,

Both of your questions come from the same idea, so let me take them in order.

Why we lean on the Desert bars

Every region tells us something, because every region's  head-count went up  while its  share  may have gone down. When a region's share falls but its population still rises, the total must have grown enough to make that possible. So each region gives us a  minimum  growth for the total - and we want the  biggest  minimum, i.e. the tightest guarantee.

The biggest share drop gives the biggest required jump. Check the 19th-20th step:

-  Desert:25%  ->  10% . For  10%  of the new total to beat  25%  of the old, the total must be at least  2.5×  bigger -> increase  > 150% .
-  Highland:32%  ->  25% . That only forces about  1.28×  -> increase > ~ 28% .

Desert's share falls the most every century, so it always sets the strongest floor. That's the only reason we use it - not because Desert is special, but because it squeezes out the largest guaranteed increase.

Why the 20th wins even though these are just minimums

You're completely right that  > 25% ,  > 60% ,  > 150%  are floors, not exact values. Here's the key: the question asks for the  most accurate statement the data forces . Compare the floors you found - they climb  25%  ->  60%  ->  150% . The 20th century's guaranteed minimum by itself ( > 150% ) already towers over what the earlier steps are even required to reach.

And notice the answer options: the 18th and 19th choices come with an  upper cap  ("less than 60%," "less than 150%") that the graph can't confirm - nothing stops those from being higher. Only  "more than 150%"  is open-ended, so only the 20th-century pairing is a statement the data actually pins down.

That's why the answer is  20th Century, more than 150% .

Answer: Dropdown 1: 20th; Dropdown 2: more than 150%

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Graphs and Tables (G&T) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards