Population Density

Correct answer: B. Different boundary definitions or reference years may be used

Explanation: Population density uses the same basic relationship: population divided by land area. Differences between reported values usually arise because sources do not always measure the same geographic unit or the same time period. One source may count only the municipal area, while another may include the wider urban agglomeration or metropolitan region.

A census year and a later estimate can also contain different population totals. These changes affect either the numerator, the denominator, or both, so the final density differs even though the method is unchanged. Option B is correct. Language does not alter a population count, area is essential to density, and reputable sources do not need different density formulas.

Correct answer: B. No because their areas may differ

Explanation: A density class on a map represents a range of people per unit area, not an exact total population. Two regions may both belong to the same class because their densities are similar or fall within the same mapped interval. However, their areas can be different, and total population depends on both density and area: \(P=D\times A\).

For example, if two regions have roughly the same density but one is twice as large, the larger region can contain approximately twice as many people. Therefore, equal map classes do not require equal total populations. Option B is correct because their areas may differ. Option A confuses density with total population, option C incorrectly says density ignores area, and option D is false because density is calculated from population and area.

Correct answer: B. When the boundary changed between years but this was ignored

Explanation: Direct answer: Option B. A density trend is meaningful only when the areas being compared are spatially comparable. If the administrative or regional boundary changes between two years and the change is ignored, the area may include different places in each year. The calculated density may then appear to rise or fall because of the boundary change rather than a real change in population concentration. Option A is not misleading because the same boundary and unit make comparison consistent. Option B is correct because an ignored boundary change can distort the trend. Option C is not a problem; knowing population and area is necessary for calculating density. Option D is also safe because the same unit makes values comparable. Memory cue: compare like with like—same boundary, same area basis, and same unit.

Correct answer: B. Analyzing percentage changes, migration, and boundary effects along with the population-to-area ratio

Explanation: The basic measure of population density is the ratio of population to area, written as \(Population\ Density=\frac{Population}{Area}\). Medium-level analysis should use this ratio but should not stop at memorizing a total or labelling every large population as dense. It should examine how density changes over time and why.

Percentage changes can show whether density is rising or falling. Migration explains movement into or out of a region, while administrative boundary changes can alter the measured ratio without an equivalent change in residents. Thus option B is most appropriate because it combines calculation with interpretation. Options A, C and D ignore area or the factors needed to understand the result.

Correct answer: B. 10%

Explanation: Answer: B, 10%. Population density means population divided by area: D = P/A. Take the original population and area as 1 each, so the original density is 1. After the changes, population becomes 1.54 times the original and area becomes 1.40 times the original. Therefore, the new density is 1.54/1.40 = 1.10 times the old density. This means density is 110% of its original value, so its increase is 10%. A is incorrect because the ratio does not produce 5%. C is the common error of subtracting 40% from 54%; percentage changes in a ratio cannot normally be found by simple subtraction. D is not supported by the calculation. Memory cue: for density, multiply the population factor by the reciprocal of the area factor.

Correct answer: B. 20%

Explanation: Answer: B, 20%. Density is population divided by area. After a 36% population decrease, the population factor is 64% or 0.64. After a 20% area decrease, the area factor is 80% or 0.80. The new density factor is therefore 0.64/0.80 = 0.80. Thus, the new density is 80% of the old density, which means it has decreased by 20%. A is not obtained from the ratio. C may result from an incorrect comparison of the two decreases. D incorrectly treats the population decrease as the density decrease. The key point is that both the numerator and denominator change. Memory cue: convert decreases into remaining fractions before dividing.

Correct answer: B. 66.7%

Explanation: Answer: B, approximately 66.7%. The phrase ‘what percentage of the higher density’ means that the lower value must be divided by the higher value. Therefore, percentage = (360/540) x 100 = 2/3 x 100 = 66.666..., which rounds to 66.7%. A would correspond to 360 being 60% of 600, not 540. C and D are also incorrect because they use the wrong ratio. Do not calculate the percentage difference unless the question asks how much one value is greater or smaller than the other. For comparison, 540 is 50% greater than 360, but 360 is 66.7% of 540. Memory cue: ‘percentage of’ uses the reference value in the denominator.

Correct answer: C. 490 persons per square kilometre

Explanation: Answer: C, 490 persons per square kilometre. ‘75% higher than 280’ means the original 280 plus an additional 75% of 280. The increase is 0.75 x 280 = 210. Adding this to the original gives 280 + 210 = 490. Equivalently, use the multiplier 1 + 0.75 = 1.75: 280 x 1.75 = 490. A is 280 x 1.5 and represents only a 50% increase. B does not follow from 75%. D would be 280 x 2 and would represent a 100% increase. A percentage is not an absolute number, so 75 cannot simply be added to 280. Memory cue: ‘x% higher’ means multiply by 1 + x/100.

Correct answer: C. 120%

Explanation: Answer: C, 120%. The basic relationship is population = density x area, because density = population/area. If density becomes 1.25 times its original value and area becomes 0.96 times its original value, multiply these factors: new population factor = 1.25 x 0.96 = 1.20. Therefore, the population will be 120% of the original population, which is a 20% increase. A ignores the density change. B would result from an incorrect combination of the percentages. D uses only the density factor and ignores the reduction in area. The wording asks for the percentage remaining, so answer 120% is correct; it also means the population increased by 20%. Memory cue: when P = D x A, multiply the density and area multipliers.

Correct answer: B. 66.7%

Explanation: Answer: B, approximately 66.7%. To find what percentage one quantity is of another, divide the first quantity by the reference quantity and multiply by 100. Here, resident density is the first quantity and daytime density is the reference: (1200/1800) x 100 = 66.666..., or about 66.7%. A, C and D use incorrect ratios or approximations. This question does not ask the percentage by which daytime density exceeds resident density. That different question would use (1800 - 1200)/1200 x 100 = 50%. Thus, the denominator must be 1800 because the wording says ‘of daytime density’. Memory cue: identify the words after ‘of’; that value is usually the base or denominator.