Read the map first,then make the argument.

Answer

Full solution

1. Compute what each district would show under each choice. By raw count, Marlow (9,000) is shaded darker than Tesk (4,000).

2. Now divide by area. Marlow: $9{,}000 \div 300 = 30$ people per square kilometer. Tesk: $4{,}000 \div 50 = 80$ people per square kilometer.

3. The two rankings are opposite. A question about crowding is a question about density, so the shading must be a ratio. The statement is true.

4. A good habit: before you accept a choropleth, ask whether the shaded value is a total or a ratio, and whether the question being asked needs a total or a ratio.

Answer

Full solution

1. An equal-area projection keeps areas true. Both lakes have the same real area, so they must have the same area on the map.

2. To keep area true while east-west distances are multiplied by $1.5$, north-south distances must be multiplied by $1/1.5$, because $1.5\times\frac{1}{1.5}=1$.

3. So Lake Quay's width is $1.5$ times Pim's width and its height is $\frac{1}{1.5}\approx 0.67$ times Pim's height. A circle drawn this way becomes an oval, $1.5\div 0.67=2.25$ times wider than tall.

4. Lake Pim at the center has no stretch, so it stays round. The pair therefore shows the key trade-off: area is preserved at the cost of shape. Choice (E) says exactly this.

5. Eliminate: choice (A) and choice (C) treat the stretch as changing area, which an equal-area map does not allow. Choice (B) claims no distortion, but every flat map distorts something. Choice (D) invents a shrinking of area.