GRE® Quant Practice | Quantitative Comparison Q4

GRE Practice Questions | Ratio and Proportion | Area of Circles, Rings

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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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 GRE Online Course - QuantTry it free! Register in 2 easy steps and Start learning in 5 minutes! Already have an Account? GRE Live Online Classes Next Batch August 26, 2022 Where is Wizako located? Wizako - GMAT, GRE, SAT Prep An Ascent Education Initiative 14B/1 Dr Thirumurthy Nagar 1st Street Nungambakkam Chennai 600 034. India Work @ Wizako How to reach Wizako? Mobile:$91) 93800 48484
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