GRE® Quant Practice | Quantitative Comparison Q4

The GRE maths sample question given below is a Quantitative Comparison Question in ratio and proportion. This GRE Math question tests the concept of Area of a Circle, concentric circles, and area of rings.

Question 4: Three concentric circles of radii 2 cm, 10 cm, and 15 cm are drawn.

Quantity A	Quantity B
Ratio of area enclosed between the outer circle and middle circle to the area enclosed between the middle circle and inner circle.	Ratio of area enclosed between the middle circle and inner circle and the area of the innermost circle.

1. Quantity A is greater
2. Quantity B is greater
3. The two quantities are equal
4. Cannot be determined

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Video Explanation

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Explanatory Answer | GRE Practice Question 4

Given Data
Radius of Inner circle r₁ = 2 cm
Radius of Middle circle r₂ = 10 cm
Radius of Outer circle r₃ = 15 cm

Formula Used
Area of circle = π × r²
where r is the radius of the circle.

Calculate the area of the three circles

Area of Inner circle A₁ = π × r₁² = π × 2² = 4π cm²
Area of Middle circle A₂ = π × r₂² = π × 10² = 100π cm²
Area of Outer circle A₃ = π × r₃² = π × 15² = 225π cm²

Step 1: Calculate Quantity A

Quantity A: Ratio of area enclosed between the outer circle and middle circle to the area enclosed between the middle circle and inner circle.

\\frac{\text{Area enclosed between the outer circle and middle circle}}{\text{Area enclosed between the middle circle and inner circle}}) = \\frac{\text{225π - 100π}}{\text{100π - 4π}})
→ \\frac{\text{125}}{\text{96}}) ∼ 1.3

Step 2: Calculate Quantity B

Quantity B: Ratio of area enclosed between the middle circle and inner circle and the area of the innermost circle.

\\frac{\text{Area enclosed between the middle circle and inner circle}}{\text{Area of the inner circle}}) = \\frac{\text{100π - 4π}}{\text{4π}})
→ \\frac{\text{96}}{\text{4}}) = 24

Step 3: The Comparison

Quantity A = 1.302
Quantity B = 24

Quantity B > Quantity A

Choice B is the correct answer