Population Density

Correct answer: C. 350 persons per square kilometre

Explanation: Population density tells us how many people live in one square kilometre. It is found by dividing the total population by the total area. The unit is persons per square kilometre, so both the population and area must be used in the calculation.

Here, density is \(525000 \div 1500\). Dividing both numbers by 100 gives \(5250 \div 15=350\). Therefore, 350 people live in each square kilometre on average. This matches option C. The other choices result from using an incorrect division or from not simplifying the figures correctly.

Correct answer: B. 3 times

Explanation: Density compares population with area. The first portion contains 50 percent of the population but only 25 percent of the area. The remaining portion contains the other 50 percent of the population over 75 percent of the area. Because population shares are equal but the first area is much smaller, the first portion is denser.

For the first portion, relative density is \(0.50/0.25=2\) times the regional average. For the remaining portion it is \(0.50/0.75=2/3\) times the average. The ratio of their densities is \(2/(2/3)=3\). Therefore, the first portion is three times as dense as the remaining portion, so option B is correct.

Correct answer: C. 6 times

Explanation: To compare the two portions, calculate each portion’s density relative to the whole-region average. The first portion contains 80 percent of the population in 40 percent of the area, so its relative density is \(0.80\div0.40=2\). The remaining portion contains 20 percent of the population in the remaining 60 percent of the area, so its relative density is \(0.20\div0.60=\frac{1}{3}\).

Now compare these two densities: \(2\div\frac{1}{3}=6\). Thus the first portion is six times as dense as the remaining portion, making option C correct. Merely comparing 80 percent with 20 percent ignores the different area sizes. The smaller area holds most of the population, which is why its density is much higher.

Correct answer: A. Arithmetic density alone does not fully show resource pressure

Explanation: Arithmetic density uses total land area, so it can hide how much land is actually productive or available for cultivation. A region may contain deserts, mountains, forests, wetlands, or other unsuitable land. If most people depend on a small cultivated area, that land can face intense pressure even when the average number of people per square kilometre of total land is low.

Therefore, option A is correct: arithmetic density alone does not fully show resource pressure. Physiological pressure gives a different perspective by relating population to cultivated land. Option B is wrong because low average density does not guarantee low pressure. Option C ignores the importance of productive land, and option D is false because arithmetic density is useful for regions as well as cities, though it has limits.

Correct answer: B. Convert both to the same area unit before comparison

Explanation: Density values can be compared directly only when their area units are the same. “Persons per square mile” and “persons per square kilometre” describe similar ideas but use different-sized area units. Because a square kilometre and a square mile are not equal areas, the numerical values on the two scales are different even when describing the same population distribution.

The correct procedure is to convert both densities to a common unit, such as persons per square kilometre, and then compare them. Only after conversion can the larger value reliably indicate the higher density. Therefore, option B is correct. Comparing the numbers without conversion may reverse the conclusion, and comparing only total population ignores the area occupied.

Correct answer: B. Population and area changes may have offset each other in the ratio

Explanation: Population density is an average ratio, not a complete description of where people live. It is found by dividing population by area. If the population and the area both change in matching proportions, their ratio can remain the same. Thus, an unchanged density does not prove that the settlement pattern is unchanged. The most appropriate conclusion is B: the changes may have offset each other in the ratio.

For instance, if population doubles from \(P\) to \(2P\) and area also doubles from \(A\) to \(2A\), the new density is \(2P/2A=P/A\). The numerical density is unchanged, even though the actual population and boundary are different. The internal distribution might also have changed, but average density alone cannot reveal that. Boundary changes can affect density when they alter area, so choice C is too absolute.

Correct answer: C. Analyzing proportional changes, spatial concentration, boundary definitions, and limitations of average density along with the population-area ratio

Explanation: Population density is commonly calculated as population divided by area, but serious analysis must examine what that average hides. A single density value may conceal crowded cities, empty regions, differences between habitable and total land, and the effects of changing administrative boundaries. Percentage change and spatial concentration are also important for comparison.

Option C is correct because it combines the ratio with proportional change, spatial patterns, boundary definitions and the limits of average density. Option A ignores area, B reduces analysis to arithmetic, and D confuses high density with a large total population. A small area can be very dense without containing many people.

Correct answer: C. 392 persons per square kilometre

Explanation: Population density is found by dividing population by area. Initially, the density is \(\text{Density}=\frac{525000}{1500}=350\) persons per square kilometre. The area does not change, so a 12 percent increase in population produces the same 12 percent increase in density. The new density is therefore \(350\times1.12=392\) persons per square kilometre. Equivalently, the new population is \(525000\times1.12=588000\), and \(588000\div1500=392\).

Thus, option C is correct. Option A is the old density before growth, not the new value. Option B does not result from applying the 12 percent increase, and option D is too high. The key point is that when area remains constant, population density changes in the same proportion as population. The unit must be persons per square kilometre.

Correct answer: C. 560 persons per square kilometre

Explanation: First find the original population from density and area. Using population = density × area, the population is 640 × 625 = 400,000 people. When 50,000 people leave, the remaining population is 400,000 − 50,000 = 350,000. The area does not change because the question describes migration out, not a boundary change.

The new density is therefore 350,000/625 = 560 persons per square kilometre. Hence option C is correct. A common mistake is to subtract 50,000 directly from the density, but people and persons per square kilometre are different quantities. The correct method is to calculate population first, subtract the migrants, and then divide by the unchanged area.

Correct answer: C. 540000 people

Explanation: Equal density means that both regions have the same number of people per square kilometre. First calculate region A's density by dividing its population by its area: \(360000\div900=400\) persons per square kilometre. Region B must also have a density of 400 because the question says the densities are equal. Its population is therefore found by multiplying this density by B's area: \(400\times1350=540000\) people.

Option C is correct. A quick check confirms the result: \(540000\div1350=400\), so B has exactly the same density as A. Option A would give a density of about 355.6, option B about 370.4, and option D about 444.4 persons per square kilometre. Only C satisfies the equal-density condition.

Correct answer: B. Increase by about 8.3 percent

Explanation: Density changes according to the ratio of the population change to the area change. A 30 percent population increase multiplies population by \(1.30\), while a 20 percent area increase multiplies area by \(1.20\). Therefore the new density factor is \(\frac{1.30}{1.20}=1.0833\). The new density is about 108.33 percent of the old density.

The increase is therefore about 8.33 percent, usually rounded to 8.3 percent. Option B is correct. Simply subtracting 20 from 30 gives 10 percent, but that ignores the fact that the changed area is the denominator and that percentage changes combine as a ratio. The calculation assumes the stated increases are measured from the original values.

Correct answer: B. 480 persons per square kilometre

Explanation: Density is calculated by dividing population by area. Let the original population be P and the original area be A, so the original density is \(540=P/A\). After the changes, population becomes \(0.80P\), because it falls by 20 percent, and area becomes \(0.90A\), because it falls by 10 percent. The new density is therefore \(540\times 0.80/0.90=480\) persons per square kilometre.

Thus option B is correct. A fall in population does not automatically produce an equal fall in density because area also changes. Here population decreases more sharply than area, so density declines from 540 to 480. The other numerical choices do not follow from applying the two percentage factors to the original density.

Correct answer: C. 612.5 persons per square kilometre

Explanation: First find the changed population and changed area. The original population is 420,000, and 70,000 people are added, so the new population is \(420000+70000=490000\). The original area is 700 square kilometres, and 100 square kilometres are added, so the new area is \(700+100=800\) square kilometres.

Now apply the density formula: \(D=\frac{P}{A}=\frac{490000}{800}=612.5\). Thus the new density is 612.5 persons per square kilometre, making option C correct. The calculation must use both the increased population and the increased area. Options A, B, and D result from inaccurate division or from failing to update one of the two quantities.

Correct answer: C. 400 persons per square kilometre

Explanation: Let the country’s total area be \(A\). A national average density of 260 means total population is \(260A\). If 35 percent is uninhabited, the inhabited part is 65 percent, or \(0.65A\). The question states that the whole population lives in this inhabited part.

Therefore, inhabited-area density is \(\frac{260A}{0.65A}=400\) persons per square kilometre. The total-area average is lower because it includes land with no residents. Option C is correct. Dividing 260 by 0.65 gives the same result, while using 35 percent as the denominator would incorrectly use the uninhabited share.

Correct answer: C. 450 persons per square kilometre

Explanation: Arithmetic density uses the total population divided by the total area. Let the total area be A. A density of 360 means the population is 360A. If only 80% of the area is habitable, the habitable area is 0.8A, and the entire population lives there. Its density is therefore \(\frac{360A}{0.8A}=450\) persons per square kilometre. Option C is correct.

The effective density is higher than the arithmetic density because the same population is concentrated on less than the total area. Dividing 360 by 0.8 gives 450. The values 400, 420, and 480 do not result from the required adjustment. This calculation assumes that the whole population occupies the habitable portion, exactly as stated.

Correct answer: A. Average density can hide local concentration

Explanation: Average density is a broad summary calculated by dividing total population by total area. It gives one overall value, but it does not show where people actually live inside the region. A region can have a moderate average while most residents are crowded into a small part and very little population occupies the remaining area.

Here, 70 percent of the population lives on only 20 percent of the land. This indicates strong internal concentration and an uneven spatial pattern, even if the regional average equals that of another region. Therefore, option A is correct. Equal average density does not prove equal distribution, equal totals, or similar settlement patterns.

Correct answer: B. 2057 persons per square kilometre

Explanation: The initial density is \(900000\div450=2000\) persons per square kilometre. An 8 percent population increase changes the population to \(1.08\times900000\), while a 5 percent area increase changes the area to \(1.05\times450\). The new density can therefore be found directly as \(2000\times\frac{1.08}{1.05}=2057.14\), approximately 2057 persons per square kilometre.

Option B is correct. Density rises because population grows faster proportionally than area. Option A is too low, while option C is a rounded value that does not match the calculation. Option D, 2160, would result from increasing the initial density by 8 percent while ignoring the area increase. The area increase partly offsets the population increase, so both changes must be included in the ratio.

Correct answer: B. 600 persons per square kilometre

Explanation: Density changes according to the relative changes in population and area. If population is multiplied by 1.20 and area is multiplied by 1.50, the new density is the old density multiplied by \(\frac{1.20}{1.50}\). Since area grows more than population, fewer people are present per square kilometre than before.

The factor is \(\frac{1.20}{1.50}=0.8\). Therefore, new density is \(750\times0.8=600\) persons per square kilometre. Option B is correct. A value such as 750 would ignore the changes, while a value above 750 would incorrectly assume that population grew faster than area.

Correct answer: C. 600 persons per square kilometre

Explanation: Density rises when the same population is concentrated in a smaller area. A 30% decrease in area means that only 70% of the original area remains. Since population is unchanged, the new density must be found by dividing the original density by the remaining area factor. This is an inverse relationship, not a direct 30% increase.

The calculation is \(D_{new}=420/0.70=600\) persons per square kilometre. Thus the new density is 600 persons per square kilometre, so option C is correct. Simply adding 30% to 420 would give 546, which is not correct because the denominator has become 70% of its original size.

Correct answer: B. 400 persons per square kilometre

Explanation: First update both quantities before calculating density. The new population is \(550000+50000=600000\). The new area is \(1250+250=1500\) square kilometres. Density is population divided by area, so the new value is \(\frac{600000}{1500}=400\) persons per square kilometre.

Thus option B is correct. It would be incorrect to divide the added population by the original area or to use the original population and area, because both quantities change in the question. The units also confirm the result: persons divided by square kilometres gives persons per square kilometre. The calculation gives an exact, not merely approximate, answer.

Correct answer: C. 444 persons per square kilometre

Explanation: Density changes when population and area change because density is population divided by area. A 25 percent population increase multiplies the original population by \(1.25\). A 10 percent area decrease leaves 90 percent of the original area, so the new area is multiplied by \(0.90\). Therefore, the new density is found by multiplying the old density by the population factor and dividing by the area factor.

The calculation is \(320\times\frac{1.25}{0.90}=444.44\ldots\) persons per square kilometre. Rounded to the nearest listed value, this is 444, so option C is correct. The result is greater than 320 because population rises while the land area becomes smaller. Option A would ignore the area reduction, and option D overstates the combined effect.

Correct answer: B. 638 persons per square kilometre

Explanation: Density equals population divided by area. A 15 percent population decrease leaves 85 percent of the original population, so the population factor is 0.85. A 12 percent area decrease leaves 88 percent of the original area, giving an area factor of 0.88. The new density is therefore \(660\times\frac{0.85}{0.88}=637.5\) persons per square kilometre. Rounded to the nearest listed value, this is about 638, so B is correct.

The density does not fall by exactly 15 percent because area also becomes smaller. The reduced area partly offsets the effect of the reduced population: fewer people are spread over even less land. Since 637.5 is closest to 638 and is conventionally rounded to it, option B follows. The calculation assumes the stated percentage changes apply to the original population and original area.

Correct answer: C. 316.25 persons per square kilometre

Explanation: Population density connects population and area through \(D=P/A\). First find the original population by multiplying the density by the area: \(275\times1600=440000\). The increase of 66,000 raises the population to \(506000\). Since the question does not say that area changes, the area remains 1,600 square kilometres. The new density is therefore the new population divided by this unchanged area.

The calculation is \(506000/1600=316.25\) persons per square kilometre. Thus option C is correct. A quick check also works: the added population alone contributes \(66000/1600=41.25\) persons per square kilometre, and \(275+41.25=316.25\). The answer must be greater than 275 because population increased while area stayed fixed.

Correct answer: B. 480 persons per square kilometre

Explanation: Answer: B, 480 persons per square kilometre. Use D = P/A. First find the original area: A = 480,000/600 = 800 square kilometres. The area then increases by 200, becoming 1,000 square kilometres. Population is still 480,000, so new density = 480,000/1,000 = 480 persons per square kilometre. A is too low and would require a larger area. B is the exact quotient and is correct. C would result from using an incorrect area of 960 square kilometres. D is also incorrect and does not reflect the full area increase. A useful check is that increasing area with fixed population must reduce density below the original 600.

Correct answer: C. 667 persons per square kilometre

Explanation: The stated density of 500 persons per square kilometre is based on the total area. Let the total area be \(A\). Then the population is \(500A\). If 25 percent is uninhabitable, the habitable area is 75 percent of the total, or \(0.75A\). All the same people live in this smaller area, so effective density is found by dividing \(500A\) by \(0.75A\).

The area \(A\) cancels, giving \(500/0.75=666.67\) persons per square kilometre. This is approximately 667, so option C is correct. The effective density is higher than 500 because the population is concentrated in only three-fourths of the original area. A value of 600 would not account fully for the 25 percent area excluded.