Podcast
Questions and Answers
A sphere is inscribed in a cube. If the ratio of the volume of the sphere to the volume of the cube is 52:125, what is the ratio of the surface area of the sphere to the surface area of the cube?
A sphere is inscribed in a cube. If the ratio of the volume of the sphere to the volume of the cube is 52:125, what is the ratio of the surface area of the sphere to the surface area of the cube?
- 12:25
- 1:5 (correct)
- 1:3
- 4:25
Quantity I: The 10th term of the sequence 2, 5, 8, ... Quantity II: The 5th term of the sequence 7, 12, 17, ... Which quantity is greater?
Quantity I: The 10th term of the sequence 2, 5, 8, ... Quantity II: The 5th term of the sequence 7, 12, 17, ... Which quantity is greater?
- The quantities are equal
- Quantity II is greater (correct)
- Quantity I is greater
- The relationship cannot be determined
If $x^2 + ax + b = 0$ has roots $α$ and $β$, and $rac{1}{α} + rac{1}{β} = 4$, which of the following could be the equation?
If $x^2 + ax + b = 0$ has roots $α$ and $β$, and $rac{1}{α} + rac{1}{β} = 4$, which of the following could be the equation?
- $x^2 - 2x + 4 = 0$
- $x^2 + 2x + 4 = 0$
- $x^2 + 4x + 4 = 0$
- $x^2 - 4x + 4 = 0$ (correct)
A mixture of 480 liters of milk and water contains 12% water. If 120 liters of water is added to the mixture, and then 120 liters of the mixture is removed, what percentage of the final mixture is water?
A mixture of 480 liters of milk and water contains 12% water. If 120 liters of water is added to the mixture, and then 120 liters of the mixture is removed, what percentage of the final mixture is water?
A standard deck of 52 cards is shuffled, and two kings are removed and replaced with two spades. What is the probability that a spade is drawn?
A standard deck of 52 cards is shuffled, and two kings are removed and replaced with two spades. What is the probability that a spade is drawn?
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Study Notes
PO Mains Level Arithmetic Questions
- Data Sufficiency: One question involving a sphere inside a cube, comparing values with a cylinder.
- Quadratic Equation: One question with an unknown constant term and unknown coefficient of x, where the constant term is found based on a condition, and the goal is to find an equation from the options with similar roots.
- Quantity Comparison: One question involving a number series with a common direction for Quantity I and Quantity II, based on an arithmetic series.
- Probability: One question involving replacing two king cards and a spade.
- Mixture and Alligation: One question involving replacing a mixture two times, with different quantities replaced in both occasions, using variables.
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